EC201 Micro Flashcards
SR v LR distinction
SR: period of time where one or more of a firm’s inputs cannot be changed
No opp.cost in SR -> one price for everything
LR: period of time in which all inputs can be changed
All opp.cost -> multiple prices
Profit Maximisation: Standard Assumption
- Profits = revenue - opportunity cost
- Objective of shareholders who control the firm and do not work for the firm
- Simple model starts with a production function or cost function
- Ignores the fact that the firm is an organisation run by people who have individual objectives and agendas
- Ignores conflicts of interest between investors and senior managers
- Competition: if a firm can at best make zero profit, it has to maximise profits to stay in business
- Incentives generated by the financial sector and the market for managers (reputation, reward packages, takeover threat)
Risk Taking
- Risk management is necessary
- Managing the risks of long term decisions is difficult
- Some incentive schemes, e.g. bonuses and stock options may encourage risk taking
- The situation is complicated by asymmetric information and incomplete contracts
- Carney: “Compensation schemes overvalued the present and heavily discounted the future, encouraging imprudent risk taking and short-termism”
PDV of Profits
- Standard assumption that firms maximise the present discounted value V of profits,
- Measuring revenue can be problematic “principally due to the accelerated recognition of commercial income and delayed accrual of costs”
- Costs are complicated if the firm has durable equipment, intellectual property or long run contracts
- Economic cost (opportunity cost) can be different from cash flows to providers of inputs and from accounting costs
Opportunity Cost (Economic Cost)
- Defined as the value of an input in its best alternative use
- For something a person or firm is buying now, the opportunity cost is the current price
- Can be impossible to measure accurately but useful to think about when making decisions
The Cost of Capital
- If you save p at interest rate r for 1 year you have cash (1+r)p next year
- If you buy the capital good, used it and sold it, you would have cash p next year
- The difference in the amount of cash is the opportunity cost of capital rp
- If p = 1 the cost of capital is r
- The cost of capital depends on: rate of physical or technical deterioration, continuation or not of technical support, technical obsolescence, changes in the price of the capital good, installation and transaction costs
- Taxes
Why do management practices differ across firms and countries?
- Good management makes a big difference to profits and other measures
- Huge variation across and within countries and industries
- Competition is associated with good management
- Monitoring, targets and incentives
Low cost of capital firms: badly managed firms?
- If capital is obsolete (ood) it may have zero or even negative opportunity cost (pay to scrap it)
- Land may have opportunity cost but that is ignored because there is no associated cash flow -> land is a fixed factor of production
- Firm may continue even though it’s making an economic loss. Low debt avoids cash flow problems
- Appointing eldest son as CEO is associated with bad management
Law of Diminishing Marginal Returns
• If one input increases while the others are held constant, the marginal product of that input falls as output expands
• Example: labour in agriculture
With a fixed amount of land, seed, machinery etc. beyond a certain point the extra output from increasing labour starts falling
Cost Functions
• The cost function c(v,w,q) is the minimum cost of producing output q using capital K and labour L with prices v and w
• This definition assumes all inputs can be varied (LR cost function)
• You find the cost function by:
Finding the levels of K and L that minimise vK + wL subject to the constraint f(K,L) > q and non negativity constraints K > 0, L > 0
• K(v,w,q) and L(v,w,q) -> sometimes called conditional fact demand as they depend on (v,w,q)
• The cost function is:
C(v,w,q) = vK(v,w,q) + wL(v,w,q)
• Check for: increasing inputs increases outputs, convexity
Properties of the Cost Function I (facts)
1) Increasing in output q
2) Homogeneous of degree 1 in input prices v,w (double price = double C(v,w,q))
3) Non-decreasing in input prices
4) Concave in input prices
5) Shephard’s lemma for cost functions
Properties of the Cost Function II
- Cost minimisation at a tangency
- If q2 > q1, producing q2 costs more than producing q1 so the cost function c(v,w,q2) > c(v,w,q1) the cost function is increasing in output
- Conditional factor demand K(v,w,q) & L(v,w,q) are homogeneous of degree 0 in input prices
- The input combination that minimises the cost of producing q does not change, but the cost of the inputs is multiplied by k
- If all input prices are multiplied by k > 0 the isocost line doesn’t change (homogeneous of degree 0)
- The cost function is homogenous of degree 1 in input prices
- If the price of K rises from vA to vB, the gradient of the isocost line changes, the cost of producing q1 increases
Thingies and Homogeneity
Thingy Homo
Isocost 0
Cost Function 1
CFD 0
Only the cost function is homosexual.
Low Wages and Labour Productivity
• Which way does causation go?
• Low production thus low wages
Or
• Low wages thus low production
• If wages are low then firms substitute labour for capital. The Marginal product of labour is then lower?
• Low productivity may be a consequence of low wages & high cost of capital
• Post financial crisis, harder & more expensive for firms to borrow. Low investment
Returns to Scale (check)
- A property of the production function
- With constant returns to scale, multiplying inputs by any m > 0 multiplies output by m so f(mK,mL) = mf(K,L)
- If f(mK,mL) > mf(K,L) there are increasing returns to scale
- If f(mK,mL) < mf(K,L) there are decreasing returns to scale
Economies of Scale
- A feature of a cost function
- Average cost AC = total cost/output
- There are economies of scale if AC decreases with output
- There are diseconomies of scale if AC increases with output
- Increasing returns to scale in the production function implies economies of scale
Volume Effects
- Capacity depends on volume
- Cost depends on surface area
- Increasing size reduces cost per unit of output
There can’t be decreasing returns to scale?
- There might be some fixed input that cannot be doubled
- There may be managerial diseconomies of scale -> management difficulties grow faster than the number of people
- The transition from a small to a large organisation can be difficult
Other influences on costs
- The production function assumes a single unchanging product and that the output from a given output is fixed by technology
- This may not be so owing to economies of scope/learning by doing
- Costs before production starts e.g. R&D, websites etc
Economies of scope
- One firm producing a range of related products has cost advantages over firms producing single products
- When a firm gains efficiencies from selling a wider range of products
- E.g. selling petrol and groceries at a petrol station (same input (labour and capital), can sell both types of goods for same pay)
Learning by Doing
• As firms build experience in producing a product the average cost of producing the product falls
Economic Loss
Economic loss is a term of art which refers to financial loss and damage suffered by a person such as can be seen only on a balance sheet rather than as physical injury to the person or destruction of property.
Isoquant
• Isoquants show the combinations of inputs that can produce a given quantity of output = indifference curves in consumer theory
The isoquant curve is a graph, used in the study ofmicroeconomics, that charts all inputs that produce a specified level of output. This graph is used as a metric for the influence that the inputs have on the level of output or production that can be obtained. The isoquant curve assists firms in making adjustments to inputs to maximize outputs, and thus profits. The curve represents a consistent level of output
Isocost
• Isocost lines show the combinations of inputs that cost the same = constant expenditure lines
In economics an isocost line shows all combinations of inputs which cost the same total amount. Although similar to the budget constraint in consumer theory, the use of the isocost line pertains to cost-minimization in production, as opposed to utility-maximization.
Conditional Factor Demand
• Conditional factor demand is the amount of inputs L and K that are needed to get output q at the least possible cost when the price of one unit of cap-Italy is v and the price of one unit of labour L, the wage, is w
• Conditional factor demand is at the point where lowest isocost line just meets the isoquant with output q
• Conditional factor demand K(v,w,q) and L(v,w,q) is the solution to the problem of minimising cost vK + wL subject to the output constraint f(K,L) > q and the nonnegativity constraints K > 0 and L > 0
• The assumption is that increasing one or both inputs increases output implies that the output constraint is always satirised as an equality so f(K,L) = q. The definition implies that for an L and K with f(K,L) = q
vK(v,w,q) + wL(v,w,q) < vK + wL
Conditional factor demands (k and l): A conditional factor demand is the cost-minimising level of an input (factor of production) such a labour or capital, required to produce a given level of output, for a given unit input cost (v/w) of the input factors
Homogeneity
- Conditional factor demand depends on the level of output and the input price ratio v/w which determines the gradient of the isocost lines
- Thus multiplying both input prices by a number m > - does not change v/w so does not change conditional factor demand
- Conditional factor demand is homogeneous of degree 0 in prices
- The cost function is homogenous of degree 1 in prices
- In summary multiplying both input prices by m > 0 does not change relative prices so does not change conditional factor demand, but does change the cost of conditional factor demand, that is the cost function, which is multiplied by m
- The cost function is increasing in output. The fact that because an increase in output requires an increase in one or both inputs and increase in output from q to q’ increases costs. Thus the cost function c(v,w,q) is increasing in output q
The Cost Function
• The cost function c(v,w,q) is the minimum cost needed at prices v and w to obtain output q or more by using a combination of inputs L and K that satisfy the nonnegativity constraints
• As conditional factor demand gives the quantities of L and K that minimise the cost needed to get output q at prices v and w this definition implies that:
c(v,w,q) = vK(v,w,q) + wL(v,w,q)
That is, the cost function is the cost needed to buy condition factor demand
• For any L and K with f(K,L) = q
• c(v,w,q) < vK + wL
Definition of Price Taking
- A firm is a price taker if nothing it can do affects the prices it pays for inputs and outputs
- In particular its output does not affect its output price
- Price taking does not mean prices do not change
- Price taking is plausible if the firm has a small market share
The Shutdown Rule
- If the cost of producing 0 is 0, i.e. c(v,w,0) = 0 the firm can make 0 profits by producing 0 so if the firm maximises profits at q > 0 profits = pq - c(v,w,q) > 0 so p > AC
- The firm shuts down if price < AC at all levels of output
- The shutdown rule implies that if a profit maximising firms produces q > 0 then price > AC
- Conventionally stated theshutdownrule is: “in the short run a firm should continue to operate if price exceeds average variable costs.” Restated, the rule is that to produce in the short run a firm must earn sufficient revenue to cover its variable costs.
The Output Rule and Marginal Cost
- Profit maximisation at q > 0 implies that marginal revenue = marginal cost
- But marginal revenue = marginal cost does not necessarily imply profit maximisation
- If MR > MC then increasing output q increases profits
- If MR < MC then increasing output q decreases profits
- The Profit MaximizationRulestates that if a firm chooses to maximize its profits, it must choose that level ofoutputwhere Marginal Cost (MC) is equal to Marginal Revenue (MR) and the Marginal Cost curve is rising. In other words, it must produce at a level where MC = MR.
What is Marginal Revenue?
- Perfect competition implies price taking
- Price taking means that nothing the firm can do changes the price
- In particular changing the firm’s output does not change the price
- Price taking implies MR = p = AR (in perfect competition case), does not depend on output
- The price may change for reasons beyond the control of the firm, e.g. an increase in demand
- For a monopoly marginal revenue depends on the firm’s output
- For a firm in an oligopoly MR depends on the firm’s output and the output of other firms
Relationship between MC and AC
- If dAC/dq > 0 same as AC is increasing when MC > AC
- If dAC/dq < 0 same as AC is decreasing when MC < AC
- If dAC/dq = 0 same as AC has a critical point when MC = AC
Profit maximisation by a price taking CRS firm
- The production function q = f(K,L) has constant returns to scale is for all positive numbers m, mf(L,K) = f(mL,mK)
- Under constant returns to scale CRS the optimal ratio of inputs (e.g. the capital labour ratio) depends on w/v
- For given w/v it is the same at all levels of output
- Multiplying inputs by 2 multiplies output by 2
- So it costs twice as much to produce 2 units of output at is costs to procure 1 unit of output
- Total cost is proportional to output
Total cost function from a CRS production function
- As total cost is proportionate to output c(q) = q c(1)
- This implies that MC = AC = c(1)
- MC and AC are equal and do not vary with output
- A firm is a price taker if nothing it can do changes the price p at which it sells
- Profits = pq - total cost = (p-AC) q
- With CRS, AC = MC does not depend on q
- If p > MC increasing q increases profits, there is no profit maximising output
- If p < MC = AC the firms makes losses at all q > 0 so produces 0
- If p = MC = AC the firm makes 0 profit at any q
- p = AC is the only price at which a price taking firm with CRS has a profit maximum at q > 0
Supply by a price taking CRS firm
- MC = AC
- Varies with input prices v and w but not with output
- In some cases the LRMC = LRAC and do not depend on q. This reflects the fact that with this Cobb-Douglas production function, with m > 0, there is constant returns to scale
- Not all CD production functions display CRS, LRMC and LRAC will generally be different from each other and vary with output q
Supply by a firm with CRS and a capacity limit
- Suppose MC and AC are equal and do not vary with output but it is impossible to produce more output than q*
- Profits = pq - total cost = (p-MC)q
- With CRS AC = MC does not depend on q
- If p < MC = AC the firm makes losses at all q > 0 so produces 0
- If p > MC = AC, so increasing q always increases profits, thus output is at its maximum level q*
- If p = AC the firm makes 0 profits at an any q
- MC and AC are equal and do not vary with output but it is impossible to produce more output than q*
Cost curves with DRS
- Under decreasing returns to scale DRS multiplying inputs by 2 multiplies output by less than 2
- So it costs more than twice as much to produce 2 units of output as it costs to produce 1 unit of output, so c(v,w,2q) > 2c(v,w,q)
- More generally with DRS, given input prices if m > 1 so, c(v,w,mq) > m(cv,w,q)
- So AC at output mq = c(v,w,mq)/mq > c(v,w,q)/q = AC output
- AC increases with output
If MC is increasing, p = MC gives profit maximum: intuition
- When q < q1, MC < p, increasing output by 1 unit increases cost by MC and revenue by p
- So long as p* > MC this increases profits
- When q > q1, MC > p*, increasing output by 1 unites increases cost by MC and revenue by p
- As p < MC this decreases profits
Profit maximisation with price taking and a DRS production function
- With DRS MC is increasing and MC > AC
- If p = MC then p > AC so the shutdown rule is satisfied
- The MC curve is the supply curve
- The firm makes profits
Cost curves with IRS
- Under IRS, multiplying inputs by 2 multiplies output by more than 2
- So it costs less than twice as much to produce 2 units of output as it costs to produce 1 unit out output, so c(v,w,2q) < 2c(v,w,q)
- More generally with IRS, given input prices if m > 1
- C(v,w,2q) < 2c(v,w,q)
- So AC at output mq = c(v,w,mq)/mq < c(v,w,q)/q = AC at output q
- AC decreases with output
Total cost function from an IRS production function
- AC decreases as q increases, there are economies of scale
- MC = gradient of tangent < AC = gradient of chord
- MC decreases as q increases
- MC = gradient of tangent < AC = gradient of chord
- MC decreases as q increases
- AC decreases q increases, there are economies of scale
AC and MC from an IRS production function
- MC < AC everywhere
- MC decreases as q increases
- AC decreases as q increases
Price taking with economies of scale at all levels of output is impossible
- Because AC is decreasing either p < AC for all q or p > AC for large q
- Where p < AC for all q, a price taking firm cannot make a profit, the shut down condition is never satisfied
- Where p > AC > MC for large q, there is no profit maximum
- A price taking firm can increase its profits indefinitely
- The firm will expand until it has a large market share and is not a price taker
Costs in an R&D intensive industry
- Total cost = F + cq
- F = R&D cost, opportunity cost before development not an opportunity cost after development
- c = constant marginal cost
- AC = F/q + c decreases at all levels of output
- If a firm has economies of scale at all levels of output, it cannot be a price taker (must be monopoly)
Price taking with economies of scale
• R&D intensive industries with a fixed development cost & constant marginal cost have economies of scale at all levels of output (because initial average cost is SO high, average falls very quickly), must have monopoly power as always incentive for more production
Cost curves and supply with a u-shaped average cost curve
- Often assumed for perfect competition
- For small q there are economies of scale, AC falls
- For large q there are diseconomies of scale, AC rises
Profit maximisation & supply with a u-shaped average cost curve
- MC decreases when q < min point of MC
- And increases when q > min point of MC
- Where AC has it’s minimum it intersects with MC
- Where p < min AC, the firm makes losses at all q > 0, the shut down condition cannot be satisfied at q > 0 so q = 0
- Where p > min AC, the firm can make profits
Long run and short run costs and supply
- Two periods: the planning and production period
- Capital is fixed in the planning period & paid for in the production period
- In the production period capital has no alternative use and cannot be sold, it’s opportunity cost is 0
- Labour is chosen and paid for in the production period
- If the firm knows in the planning period what output and oinput prices will be in the production period it can choose capital optimally and K and L are chosen to minimise total cost c(v,w,q)
- If the firm was uncertain in the planning period about prices in the production period capital may turn out not to be optimal in the production period
- If in the planning period the firm knows output q and input prices w & v in the production period it chooses the cost minimising point on the long run expansion path
- Total inputs (L,K) total cost LRTC = c, when output is q
Short run costs
- The firm installs K in the planning period, when it is uncertain what input prices will be and how much it will produce in the production period
- The cost s(v,w,K,q) of production depends on input prices v and w, capital K and output q
- It is called short run total cost (SRTC)
- Constraint LRTC c(v,w,q) does not depend on K
LRTC v SRTC
- With capital fixed at K1 in the planning period, the firm is on the short run expansion path in the production period
- At output q1 the firm is on the long run expansion path
- At other outputs the firm is not on the long run expansion path
- LRTC < SRTC always
- With a minimisation problem you can often do better and never do worse with more flexibility
- Long run (choose K and L) more flexible than short run (choose L, K fixed)
- So either LRTC < SRTC or LRTC = SRTC
Long run and short run costs and supply with a Cobb-Douglas production function
- LRTC = c(v,w,q)
- LRAC = c(v,w,q)/q
- LRMC = dc(v,w,q)/dq
- SRTC = s(v,w,K*,q)
- SRAC = s(v,w,K*,q)/q
- SRMC = ds(v,w,K*,q)/dq
- Long run average and marginal costs are equal and do not depend on output
- Short run average and marginal costs depend on output
Fixed and variable costs with the Cobb-Douglas production function
- In the production period K* cannot be varied so is not an opportunity cost
- As SRVC does not include K which is fixed in the SR, SRTC > SRVC
- SRAVC is increasing in q so SRMC > SRAVC
- Taking input prices v and w as given
- Short run total cost = F + V(q)
- The fixed cost F is not an opportunity cost in the SR
- The variable cost V(q) is an opportunity cost in the SR
Short run profit maximisation
- Short run costs have two components
- The fixed cost of capital which is determined in the planning period
- The variable cost of labour which is determined in the production period
Short run costs
- Assume that there is no alternative use of capital and it cannot be sold in the production period
- Then in the production period capital is not an opportunity cost
- The opportunity cost of production is the variable cost
Short run profit maximisation
- Output rule p = SRMC
- Shutdown rule p > SRAVC
- SRMC is the derivative of SRTC and also of SRVC with respect to q
- Output rule p = SRMC
- Shutdown rule p > SRAVC
- SRMC is the derivative of SRTC and also of SRVC with respect to q
- The firm would plan to produce 0 if it knew in the planning period that p < po
- If the firms finds in the production period that p > 0, it produces q > 0 even if p < po
- It makes an economic profit • Whether it makes an accounting loss depends on the accounting treatment of capital
- Whether it loses cash depends on debt servicing and other obligations
- Firms that can’t meet their debt obligations face bankruptcy
The General relationship between SR & LR and AC & MC
- SRAC > LRAC for all q
- SRAC = LRAC and SRMC = LRMC at output q* where the capital stock K* is at the level it would be at if K and L could be chosen freely
- Perfect competition does not imply LRAC = SRAC = LRMC = SRMC
- MC & AC are different at q*
- LRAC = SRAC = LRMC = SRMC only when capital stock is at the level that minimises the long run average cost of producing qo where qo is the level of output that minimises LRAC
What happens to firms that can’t meet their debt obligations, face insolvency (bankruptcy)?
- Complete shut down, with no sale of anything
- Completely shut down with saleable assets
- Sold as a going concern
- In insolvency the debt holders may get some money, shareholders get nothing
Long run and short run costs and supply with a fixed proportion production function
- Work in the same was as perfect complements utility functions
- Increasing L does not change q, isoquant is a horizontal line
- Increases K does not change q, isoquant is a vertical line
- Cost minimisation is at the kink
- In the short run the firm has a constant MC and a capacity limit
- If p < w = SRAVC, firm can’t cover its SRAVC cost & shuts down
- If p = w, firms makes 0 economic profits
- SR capacity limit, SRMC = SRAVC = w
- In the planning period the firms knows that in the production period p < w + v/3 it does not invest in K and shuts down
- If in the production period it turns out the w < p the firms produces its maximum output 3K*, even if p < w + v/3
- In the production period capital is a sunk cost, so is not an opportunity cost
Is the short run long run analysis useful?
- Captures the idea that unexpected things happen and if a firm has to decide on some inputs in advance it may maximise economic profits by producing even if it makes an accounting loss
- Existing firms typically have assets in place so are not in a textbook LR situation
- They also make forward looking decisions which take the assets in place into account
Why AVC?
A firm would choose toshut downifaverage revenueis below average variable cost at the profit-maximizing positive level of output. Producing anything would not generate revenue significant enough to offset the associated variable costs; producing some output would add losses (additional costs in excess of revenues) to the costs inevitably being incurred (thefixed costs). By not producing, the firm loses only the fixed costs.
Price Taking Firms
- Perfect competition implies price taking, nothing a firm does affects the prices it gets for output and pays for inputs, in particular its output does not affect price
- Nothing a purchaser does affects the price it pays for output
Standard models of perfect competition
- Short run supply curves, without entry and exit in the short run
- Long run supply curves, with entry and exit in the long run
- Implicit assumption: firms renew their capital stock in the time span over which entry & exit are possible
EC201 models of perfect competition
- Short run supply curves, without entry and exit in the short run
- Long run supply curves, with entry and exit in the long run
- Implicit assumption: firms renew their capital stock in the time span over which entry & exit are possible
When is price taking plausible?
- A homogeneous good, all firms produce an identical product
- Large number of buyers and sellers each with a small market share
- Everyone can observe prices
Entry and Exit?
- P = MC follows from profit maximisation
- P = AC follows from entry and exit equilibrium under strong assumptions
- Profit maximisation implies firms minimise total cost of output produced
- Can’t max revenue as not a price taker
- Profit maximisation does not imply that firms produce level of output that minimises AC
Markets with price taking firms
- In an equilibrium with a fixed set of price taking firms, each firm supplies a profit maximising level of output given input and output prices
- The market clears, that is supply = demand
- Entry and exit is impossible
Supply and demand with CRS
- Firm & industry supply with CRS & identical firms
- MC = AC does not depend on output
- Input prices do not vary with industry output
- With horizontal supply, price has to be at MC = AC which do not vary with output
- Firms make 0 profits
Supply and demand with constant MC=AC and a capacity limit
- MC and AC are equal and do not vary with output, but it is impossible to produce more output than q*
- Firm & industry supply with constant MC = AC and a capacity limit
- Supply & demand with constant MC = AC and a capacity limit
- Where output is below capacity, p = MC = AC which does not vary with output
- Firms make 0 profits
- Where output is at a capacity, p > MC = AC which do not vary with output
- Firms make profits and entry is likely
Entry and Exit with price taking firms
- Drop the assumption that the number of firms is fixed
- In reality prices in the future are uncertain
- Price taking firms make decisions on entry, exit and capital investment depending on their beliefs about prices in the future
A very simple model of entry and exit
- Work with simplest model, a price change is either temporary, there is no entry and exit, firms are on short run supply curves
- Or permanent, in which case firms are on long run supply curves, firms enter if they can make economic profits at the price, and exit if they make economic losses at the price
Entry and exit equilibrium
- Each firm supplies a profit maximising level of output given input and output prices
- The market clears at supply = demand
- The number of firms in the industry and industry price are at a level where no firms in the market make losses, no firm outside the market could enter and make profits > 0
- The number of firms in the industry is at a level where no firms in the market make losses, implies that p > AC for firms in the market
- No firms outside the market could enter and make profits > 0 implies that p < AC for firms not in the market
- If (a very strong assumption) all firms including potential entrants have the same costs then entry and exit equilibrium implies profit = 0, p = AC for all firms
Implications of perfect competition for price, MC & AC
- P = MC for all firms
- Implied by profit maximising by price taker
- P = AC for all firms only if there is entry and exit, all firms including potential entrants have the same costs
Entry and exit in an industry with a fixed proportions production function
- Firms & industry supply with constant MC = AC and a capacity limit
- Supply & demand with constant MC = AC and a capacity limit
- Where output is below Q*, p = MC = AC which do not vary with output, firms makes 0 profits
- Where output is at capacity, p > MC = AC which do not vary with output, firms make profits
- Firm supply with fixed proportions: q* = SR firm capacity s = SRMC = SRAVC, c = LRMC = LRAC
- Q* = SR industry capacity
- When demand = price = c = LRMC = LRAC firms make 0 profits
- Both LRS and SRS = demand
- Industry = Q*
- Quantity = q*
- Industry is in entry and exit equilibrium
- Rise in demand, SR price rise, no change in Q, profits > 0
- If demand is expected to continue at this level in LR either firms expand capacity or there is entry
- If capacity (Q) expands, the SRS curve moves out
- Price returns to c, firm makes 0 profits
- Fall in demand SR price falls, no change in Q, s < p < c
- In SR firms make economic profits (p > SRAVC)
- If demand is expected to continue at this level in LR either firms shrink capacity or there is exit
- Industry SRS moves inwards, Q falls and price returns to c
- Demand falls onto horizontal SRS curve, SR price falls to s, Q falls, SR firms make 0 economic profits (p = SRAVC)
- If demand is expected to continue at this level in LR either firms shrink capacity or there is exit
- Industry SRS moves inwards, Q falls and price returns to c
Uncertain supply or demand
- K is chosen in the planning period, based on expected price in the production period
- But it may be impossible to predict the prices due to unpredictable fluctuations in supply and demand
- In this example, the firm is never on its LRS supply curve, price fluctuates around the LR equilibrium price
- Supply uncertainty: quantity targeted at Q* in the planning period but varies in the production period therefore the price varies
- Demand uncertainty: quantity targeted at Q* in the planning period but demand varies and price fluctuates
- In these examples p is never equal to LRMC
- But p = average LRMC
Entry & exit, short run & long run costs, with a u-shaped average cost curve
- Assume all firms including potential entrants have the same costs
- Profit maximisation implies p = MC
- Assume identical firms, including potential entrants so entry and exit equilibrium implies p = AC
- P = MC = AC implies firm output is at minimum AC
- Industry output Q given by supply = demand at price p
- No. Of firms = Q/q
- If capital stock is at a level that minimises the LR cost of producing q, where q is not at the level of output that minimises LRAC
- Then at q*, LRAC = SRAC & LRMC = SRMC
Supply and demand with u-shaped AC curve
- Special case, capital stock is at the level that minimises the cost of producing q, where q is the level of output that minimises LRAC
- In this case only LRAC = SRAC = LRMC = SRMC
- Assume that all firms are identical and input prices do not vary with the size of the industry
- Each firm’s stock of capital is optimal for the output q which minimises LRAC
- Firms enter if p > min AC = P and exit if p < min AC = p
- Short run supply is the horizontal sum of firm short run supply
Long run supply with u shaped average cost curves
- Long run supply comes from entry
- Because input prices are assumed not to change as the industry changes size, LRS is a horizontal line at p
- Long run supply is perfectly elastic
- When both LRS and SRS = demand the industry is in entry and exit equilibrium
- Demand falls, in the SR there is no exit
- Firms produce less and make losses relative to LRTC by not SRVC
- The industry is not in entry and exit equilibrium
- If the fall in demand is expected to persist there is exit, industry SRS shifts inwards, industry output falls and price returns to initial level
- It is plausible that if the industry is in entry and exit equilibrium and demand & input prices don’t change it stays there
- But changes in demand or in input prices with a fixed number of firms and no entry and exit move the industry away from entry and exit equilibrium
Increasing cost industries
- If input prices rise as the industry expands, long run supply is upward sloping, but firms make 0 profits
- A fall in demand results in a fall in input prices
Decreasing cost industries
• Innovation is important
Firms with different costs and economic rent
- Different firms may have different costs due to different technologies or access to different quality inputs
- Different firms may be managed more or less well
Case 1: Entry Costs
- There is a cost to entering the industry. For firms already in the industry this is a sunk cost and not an opportunity cost
- For potential entrants this is an opportunity cost
- If at the industry price 0 < profits for firms in the industry < entry costs, firms in the industry make positive profits in entry and exit equilibrium
Case 2: some firms have higher quality inputs which can’t be traded
- Some inputs come in different qualities
- If either the difference can’t be observed so high and low quality inputs trade at the same price, or it is not possible to trade the inputs, firms with higher quality inputs have lower costs and higher profits
Case 3: some firms have higher quality inputs that can be traded
- Higher quality inputs have higher prices
- Is the simplest case all the extra profits that firms have with high quality inputs that can’t be traded go into the price of these inputs
- Now firms with high quality inputs make 0 profits
Economic Rent
- Originally this story about different quality inputs was about farming with varying land quality
- With no market for land, farmers with high quality land make economic profits
- With a market for land, all the profits go to the land owner in the form of rent
- Rent sometimes means profits
A very simple model of rent in a price taking oil industry
- There are two types of input
- High quality onshore wells, MC = AC = c1, total capacity Q1
- Low quality offshore wells, MC = AC = c2 > c1, total capacity Q2
- p < c1, no production
- p = c1, onshore produce between 0 and Q1, offshore 0
- c1 < p < c2, onshore produce Q1, offshore 0
- p = c2, onshore produce Q1, offshore between 0 and Q2
- p > c2, onshore produce Q1, offshore produce Q2
- When there are firms with different costs and the low cost firms have limited capacity, the low cost firms may make profits in entry and exit equilibrium
- Where offshore firms make profits, firms with higher costs may find it profitable to start production
Perfect competition with entry & exit
- Simple model - all firms in the industry have the same costs and make zero economic profits
- Mechanism, high cost firms imitate low cost firms, high cost firms go out of business
- In previous model, high cost firms can survive if the number of low cost firms is limited and demand exceeds the output of low cost firms
Perfect competition: the marginal firm
- The marginal firm in an industry makes zero profits
- There may be more than one marginal firm
- Firms with lower costs make profits
Quotas: limits on output
- Situation with no quota: consumer surplus
* Quota, limiting output: consumer surplus, producers make profit (rent), deadweight loss (loss CS - profits)
Welfare economics of a tax with supply and demand
- Assume that firms’ costs = social costs
* A strong assumption requiring no externalities and perfectly competitive input markets
Produce surplus for a firm
- Total cost = F + V(q) = fixed cost + variable cost
- V’(q) = derivative of variable cost = MC
- Integration V(q1) is area under MC curve
- Total revenue = p1q1
- Producer surplus = total revenue - variable cost
- If there is no fixed costs, produce surplus = profit
- The tax t per unit increases marginal cost by t
Effect of a tax in industry with CRS
- If the tax is t and price paid by consumers is p, firms get p-t
- If all firms have CRS so constant AC & MC, profits from supplying are (p-t-c)q
- Profits are 0 when p = c+t
- Supply with tax is perfectly elastic at c+t
- Assuming that input prices don’t change when the industry expands, industry supply with the tax is horizontal at c+t
Effects of an excise tax with CRS
- With no tax price is c (= AC = MC), industry produces Q1, with the tax price c + t, industry produces Q2, tax revenue = tQ2
- With CRS there is no producer surplus
- With no tax price = c, industry output = Q1
- With tax t price = c + t, Q falls to Q2
- Loss consumer surplus > tax revenue
Definition of deadweight loss due to tax
- Loss of producer & consumer surplus - tax revenue
- Loss of consumer surplus approximately = equivalent variation
- Deadweight loss approximately = equivalent variation - Tax revenue = excess burden of the tax to the consumer
Implication
- Given target tax revenue it is better to raise tax revenue by taxing goods whose demand is inelastic
- But this ignores distribution
- If the good is a large proportion of the consumption of poor people and you want to take this into account this argument is too simple
The UK debate on alcohol
- Externalities: harm to others, medical costs
- Alcohol taxes not well decided
- Most effective policy for reducing consumption is increasing the price
- A minimum price results in larger transfers to supermarkets & brewers
- Taxes raise government revenue
- How far supermarkets & brewers absorb the tax is an empirical question
Perfect competition
- There is price taking
- Find marginal revenue = price
- Find firm supply as a function of price
- Equate totally supply by all firms to demand
Price discrimination
- Up to now p = price per unit same for all buyers, doesn’t depend on who the buyer is and how much purchased
- Now suppose p = p1 for lucky people, p = p2 > p1 for others
- If the lucky people can sell on to the others at p with p1 < p < p2 they make a profit and no one buys at p2
Dropping the one price assumption
- If it is impossible, costly or difficult to resell, people may end up paying different unit prices for the same good
- This is called price discrimination
First Degree (Perfect) Price Discrimination
- Suppose there is one consumer: V(q) (value) is the most the consumer will pay for q1 units
- Assume constant marginal cost c so the cost of producing q is cq
- The monopoly makes a take it or leave it offer to the consumer, either get q for a total payment of just less than v(q) or get nothing
- Consumer accepts offer because payment < value
- Monopoly profits V(q) - cq
- Recall V’(q) is the downward sloping demand curve if the consumer is a price taker so the foc V’(q) = c gives a maximum
- Monopoly has to know the function V (q) to make the profit maximising offer
- Compared to perfect competition there is no loss of surplus, but all the consumer surplus now goes to the monopolist
- Suppose there are 2 consumers
2 consumers
- V1(q1), V2(q2) is the most the consumers will pay for q1 and q2
- Assume constant marginal cost c, so the cost of producing q1 + q2 is c (q1 + q2)
- The monopoly makes a take it or leave it offer to consumer 1 either get q1 for a total payment of just less than v1(q1) or get nothing. Similarly for consumer 2
- Consumers accept offer because payment < value
- Monopoly profits: V1(q1) + V2(q2) - c(q1 + q2)
- Foc: V’1(q1) = c, V’2(q2) = c
- As V’1(q1), v’2(q2) are the downward sloping demand curve if the consumer is a price taker so the foc will give a maximum
- The monopoly has to know the value functions V1(q1) and V2(q2) to know how much to charge the consumer
- With more consumers, the monopoly has to know the value of function for each consumer - a lot of information
- Online history & loyalty cards generate information
Quantity (Second Degree) Price Discrimination
- Make the price per unit vary with the amount purchased
- E.g., Quantity discounts, 2 for 1 offers
- The customer’s choice of quantity is informative about demand and consumer surplus although it does not reveal everything
- Sellers can take advantage of this
Multi-market (Third Degree) Price Discrimination
- Suppose customers can be sorted in some way, e.g. where they buy (online or shop), when they buy, age, student status
- Then the firm can charge different prices to different groups and make more profit than if it had to charge everyone the same price
- Multi-market price discrimination maximises total revenue - total cost
- R1(q1) + R2(q2) …. Ri(qi) - c(q1 + q2 …. + qi … + qn)
- First order conditions for maximisation set derivative with respect to qi at 0 so R’i(qi) = c’(q1 + q2 …. + qi … + qn) for all I
- Marginal revenue is the same in all markets and equal to marginal cost
- The mark up over marginal cost is higher when e is smaller
- Intuition: when demand is inelastic, increasing price reduces demand by less
Information requirements for monopoly
- Single market: price elasticity of total demand
- Multi-market: price elasticity of demand in each market
- Perfect price discrimination: entire demand curve of each individual
- Quantity discrimination: can set up a situation where a consumer’s choice of contract reveals information about the individual but this is not as profitable as a situation where the monopoly already knows the information
Game Theory
- This is the way modern economists model oligopoly (industries with a small number of firms who take into account each other’s actions
- Games have players
- Each player has a strategy
- Payoffs depend on strategies and illustrated in the payoff matrix
- The players are firm 1 and firm 2
- The players’ strategies are large output & small output
- The payoff for each player depends on the choice of strategy by all players
- The table is the payoff matrix
- Think of this as a model of a cartel
- Limiting production increases profits for all firms
- But each firm has an incentive to increase output
- Cartels are difficult to sustain
Prisoner’s dilemma
- Player 1 and player 2 are prisoners
- They are both interrogated and offered a reduction in prison sentence to anyone who confesses
- Both have an incentive to confess, but they both do worse if they both confess than they would if neither confessed
Lessons from Game Theory
1) In the standard competitive model, people acting individually in their own self interest achieve a Pareto efficient outcome
In the prisoner’s dilemma model the opposite happens, the outcome when both act in their individual interest is worse for both of them than if they act cooperatively
2) In sport, games are zero sum, one team’s win is another team’s loss
Prisoner’s dilemma in not zero sum (neither is life)
Dominant strategy and Cournot-Nash equilibria
- A strategy is dominant if it maximises a player’s payoff whatever the other player does
- In prisoner’s dilemma both players have a dominant strategy, confess
- The prisoner’s dilemma has a dominant strategy equilibrium, i.e. a situation in which each player has, and plays, a dominant strategy
- Many games do not have a dominant strategy equilibrium
Definition of a Cournot-Nash equilibrium in a duopoly model
- In the Cournot model of a duopoly (industry with 2 firms) each firm’s strategy is its output
- In the Cournot-Nash equilibrium the outputs q1 and q2 have the property that given q2 firm 1 maximises its own profits by choosing q1 given q1 firm 2 maximises its own profits by choosing q2
Reaction functions and cartels
- In a 2 firm cartel with the same cost and demand functions
- If firm 2 sticks to the cartel output, firm 1 can increase profits by increasing output
- If firm 1 sticks to the cartel output, firm 2 can increase profits by increasing output
- If both firms increase output, both make lower profits than with the cartel
- Cartel agreements are hard to sustain, particularly if output is unobservable09 or if the cartel is illegal
Nash Equilibrium
- Cournot Nash equilibrium is special case of a Nash equilibrium
- In a Nash equilibrium each player’s strategy maximises his payoff, given the strategies pursued by the other players
- In a Cournot model the strategy is output
Nash equilibrium and dominant strategy equilibrium
- In prisoner’s dilemma confess is a dominant strategy, because it is the best thing to do whatever the other player does
- In a dominant strategy equilibrium each player has and plays a dominant strategy
- A dominant strategy equilibrium is always a Nash equilibrium
- But a Nash equilibrium is generally not a dominant strategy equilibrium
Bertrand Nash equilibrium
- In a Bertrand duopoly game price is the strategic variable
- Suppose 2 firms produce an identical good and both have total cost cq so AC = MC = c
- If both firms charge the same price p they share the market equally
- If one firm charges a lower price it takes the entire market
- If firm 1 charges p1 > c, firm 2’s best response is to charge p2 > c where p2 is just less than p1
- Firm 1 sells nothing and makes 0 profits, but firm 1 could do better by charging just less than p2, so p1, p2 is not a Nash equilibrium
- If either firm charged less than c it makes losses and could do better by Charing c
- The Bertrand Nash equilibrium has p1 = p2 = c
Comparing Bertrand and Cournot
• Which model is appropriate depends on the real world situation we are trying to understand
• The result that price setting gives the same result as perfect competition does not hold if:
the goods the firm produces are not perfect substitutes
Or firms commit to quantity (capacity) before they set prices
Pure and mixed strategies
- A player plays a pure strategy if she does not randomise e.g. she always patrols or always doesn’t patrol
- A player plays a mixed strategy if she randomises, e.g. she always patrols with probability 1/3 and doesn’t patrol with probability 2/3
- The enforcement game has no equilibrium in pure strategies
- The enforcement game has no equilibrium in pure strategies but does have an equilibrium in mixed strategies
- This game has an equilibrium in mixed strategies where the warden patrols with probability 0.1 & the driver parks legally with probability 0.75
- Note: in the equilibrium in an mixed strategies, the probability that the warden patrols is determined by the driver’s indifference condition the probability that the driver parks legally is determined by the warden’s indifference condition
- Do all games have an equilibrium in either pure or mixed strategies?
- Yes, if the game has simultaneous moves and there are a finite number of players who each have a finite number of pure strategies
- There are games in which there is no equilibrium in pure strategies, so in the Model players must randomise (e.g. sports hit right or left to keep opponent guessing)
Multiple Equilbria
- Games have multiple equilibria, so a game theoretic model may not give a prediction of the outcome
- This is especially true if the same players play many times
Simultaneous and sequential move games
• Simultaneous move game (normal form): players choose their strategies simultaneously and used a payoff matrix to illustrate the game
Sequential move game (extensive form): simple version has 2 stages -> stage 1) potential entrant chooses whether to enter, 2) incumbent chooses whether to fight
• Extensive form games are analysed using a game tree
• In (a,b), a = potential entrant’s profit, b = incumbent’s profit
• If the potential entrant does not enter, the incumbent has no choice to make
• Potential entrant gets 0, incumbent has 9
• If the potential entrant enters stage 1, what does the incumbent do at stage 2? -> not fight as gets -1, 1 if not fight?
• What does the potential entrant do at stage 1? Enters
• In the entry game, the incumbent would like to commit to fighting if there is entry so as to deter entry
• But the commitment is not credible because once there is entry it is not profitable to fight it
• Commitment can be strategically useful
• Commitment strategies, in the entry game investing in capacity to reduce marginal cost
• The entry game looked at a simultaneous move game, has two Nash equilibria (not enter, fight) & (enter, not fight)
• Looking at this as sequential move game it has one equilibrium (enter not fight)
• Always analyse sequential move games by backward induction
• What does the last player to move do, given what other players have already done?
• What does the next to last player to move do, given what other players have already done, and knowing how last player to move will respond?
• What does the first player to move do knowing how players will respond in all future moves?
Stackelberg Equilibrium
- There are two firms 1(leader) and 2(follower) with costs cq1, cq2
- P = a - b(q1 + q2)
- Cournot assumes q1 and q2 are chosen simultaneously
- Stackelberg assumes 2 stages
- Stage 1 leader chooses q1
- Stage 2 follower chooses q2
Comparisons
- Price and industry profits re highest in monopoly and lowest with perfect competition
- As n, the number of firms in a Cournot-Nash model, gets larger, price falls, industry output increases, industry profits fall
- When n is very large, price, industry output and industry profits are close to their perfect competition levels
- Comparing Stackelberg and 2 firm Cournot-Nash, in Stackelberg price is lower, industry profits are lower, leader’s profits are higher, follower’s lower than in CN
A two stage entry game
- At stage 1 firms decide whether to enter the market or not, if they enter they pay F
- At stage 2 they have MC = AC = c and they play a Cournot - Nash Oligopoly game with p = a - bQ, where Q = q1 + q2 … + qn
- The number of firms is small if there is a large fixed or marginal cost, or demand is small (a small or b large)
Why is this stage 2 game important?
- This is a simple model of product cycle
- Stage 1 decides whether to start on product development
- Stage 2 brings product to the market
- Decisions at stage 1 depend on what is expected to happen at stage 2 (patent laws matter)
- Think of the fixed cost as R&D
- High R&D costs result in fewer firms in the industry
- Firms that commit early have first move advantages
- Firms that commit late may learn form the others’ mistakes
Repeated games
- With prisoner’s dilemma, if game is played once, confess is a dominant strategy for both players
- If the game is repeated 10 times does this change things?
- The situation is different when game is repeated an infinite number of times, and the aim is to maximise present discounted value of payoffs
- In the trigger strategy start bu not confessing
- If both players have not confessed in rounds 1,2..n, do not confess in rounds n+1
- If either player has confessed at some point in rounds 1,2,…n, confess in round n+1
- Both players playing the trigger strategy is a Nash equilibrium repeated game if the discount factor is not too small
- In the equilibrium players have no incentive to deviate from the trigger strategy at any point, i.e. their commitment to the strategy is credible (equilibrium is sub-game perfect)
- Trigger strategy depends on being able to obverse what other players do
- It is hard to sustain co-operation where cheating is unobservable
- The trigger strategy can be a disaster when misperception is possible
