Term 1 Week 9: Costs of Production Flashcards
What is the difference between explicit and implicit costs (2)
-Explicit costs are costs needing a direct monetary outlay
-Implicit costs are costs not involving such a monetary outlay
What are economic, accounting and sunk costs (2,1,2)
-The economic cost of an input is its opportunity cost, both explicit and implicit
-This is a forward looking concept, depending on the decision made and current market prices
-Accounting costs are all explicit, incurred in the past
-Sunk costs are costs already incurred, so they shouldn’t affect future decisions and can’t be avoided
-However, they may irrationally still have an impact (if you buy a cinema ticket and find it boring would you still stay because the cost)
How can firms aim to maximise profits, and how can we solve this with equations (3,2)
-Total revenue = TR = PQ = Pf(K, L)
-Total cost = TC = wL + rK (w and r are the cost of labour and capital)
-Profit = π = Pf(K, L) - (wL + rK)
You can:
-Choose Q, K, L to maximise π
-Minimise costs for a given output level Q0 then choose output to maximise π
What is an Isocost curve (2)
-An isocost curve are all the combinations of labour and capital that a producer could afford to purchase at a given set of input prices
-The slope of the curve = w/r ((TC/r) / (TC/w) remember)
How to set up a lagrangian for the firms’ cost minimisation problem (1, 3, 1, 3, 3, 1)
-∇ = wL + rK + λ(Q0 - f(L, K))
(Then set up FOC’s)
-∂∇/∂L = w - λ(dF/dL) = 0
-∂∇/∂K = r - λ(dF/dK) = 0
-∂∇/∂λ = Q0 - F(L,K) = 0
(Divide FOC 1 by 2)
-w/r = (dF/dL)/(dF/dK) = MRTS
(Rearrange with λ)
-(dF/dK)/r = (dD/dL)/w = λ
-The lagrange multiplier (λ) shows how much the optimal value of the objective function changes following a change in the constraint
-How much costs increase when output constraint increases marginally
-L* = L(r, w, Q)
-K = K*(r, w, Q)
-These are the conditional factor demands, as they both depend on Q
-TC(r, w, Q) = WL(r, w, q) + rK(r, w, Q)
How to solve the firms cost minimisation problem (5)
-min wL + rK subject to f(L, K) = Q0
-Shift the isocost until it is tangential to isoquant
-Slope of isoquant = slope of isocost (MRTS = w/r)
-You need to reach both the technically efficient and cost minimising point
-The rate at which K can be traded for L in the production process and marketplace is the same
How to represent a firms cost minimising problem with a cobb douglas function (2,3,2,2,1)
-Q = LaKb
-∇ = wL + rK +λ(Q0 - LaKb)
-d∇/dL = w - λaL(a-1)Kb = 0
-d∇/dK = r - λbLaKb-1
-d∇/dλ = Q0 - LaKb
-w/r = aK/bL
-K = L(w/r)(b/a)
-L* = Q0(1/a+b)(ar/bw)(b/a+b)
-K* = Q0(1/a+b)(bw/ar)(a/a+b)
-TC = wQ0(1/a+b)(ar/bw)(b/a+b) + rQ0(1/a+b)(bw/ar)(a/a+b)
What is the expansion path (3)
-The expansion path is the set of optimal combinations of L and K (tangency of isoquant and isocost)
-This shows how inputs increase with increases in output (outward shift of isoquant curve)
-The expansion path does not have to be a straight line nor start at the origin
How can you get corner solutions with isocosts/quants (4)
-You can also get a corner solution if every dollar spent on L/K is more productive than every dollar spent on K/L
-In this case, the tangency solution doesn’t hold since the isocost is flatter than the isoquant at all points
-MPL/MPK > w/r, MPL/w > MPK/r
-Every dollar spent on labour is more productive than every dollar spent on capital
What happens when the price of an input changes for isoquants/costs (2, 2, 1)
-When we change the price of one of our inputs, we are not pivoting the isocost curve around the intercept, but around the isoquant
-An increase in w means the isocost becomes steeper, the new optimal point is further up the isoquant, and the firm uses more capital and less labour
For this, we need to assume
-convex isoquants
-K, L > 0
-To keep output constant, there will need to be an increase in the cost of production
What are average costs and marginal costs (2,2)
-Average cost reflects costs per unit of output
-AC(r, w, Q) = C(r, w, Q)/Q
-Marginal cost reflects the change in total costs following a change in output
-MC(r, w, Q) = ∂C(r, w, Q)/∂Q
How can we represent being technologically and economically efficient on isoquants (2,3)
-All input bundles on an isoquant produce a certain amount of units without wasting units
-This shows the different technologically efficient ways of producing a certain amount of units
-To be economically efficient, the inputs have to be the least costly way of reaching the given output level
-For every output quantity, there is usually one such economically efficient input bundle where TRS = -w/r
-When technology is homothetic, the economically efficient input bundles lie on the same ray from the origin
How do cost functions change depending on the production function (4)
-A concave production function yields a convex cost function
-An IRS production function at all Q has a continually falling AC curve (MC<AC at all Q)
-A production function that is concave for +Q but requires a fixed cost has a U shaped AC curve, reaching a minimum then rising, pulling the MC up
-A non-concave production function yields a decreasing then increasing cost function (TC rise more rapidly once diminishing returns set in)
How to graphically represent IRS vs DRS on different graphs (2,1,1)
-On an isoquant graph, IRS occurs where the rise in the isoquant (10 -> 40 for output = 4x) is greater than the rise in factor inputs (2.5 -> 5 for L, K = 2x)
-DRS then returns when the rate rise in output (upwards shifts in the isoquants are less than the x rises in the factor inputs (remember all cost minimizing outputs lie on the same ray)
-With a total cost curve (output on the x axis, cost ($) on the y), there are IRS when the curve is concave, and DRS when the curve is convex
-With an AC/MC curve (output c axis, cost y axis), DRS occur at the bottom of the AC curve, where MC=AC
What are some rules about the isocost curve and shifts (2)
-Any change in tech/input prices will shift the isocost curve and hence the production function
-The higher the isocost curve, the higher total costs
What is the relationship between AC and MC (3,1)
-When AC is decreasing in Q, AC > MC
-When AC is increasing in Q, AC < MC
-When AC is at a minimum, AC = MC
-The marginal always controls the average
How can we rewrite total cost in the short run (2)
-TC = wL + rK_, where kbar represents the fixed amount of capital
-The cost of labour constitutes the firms total variable cost, the cost of capital constitutes the firms total fixed cost
What is the short run expansion path (2)
-In the short run, firms can;t substitute between inputs, so optimality may not involve a tangency
-The short run expansion path is a horizontal line representing how firms can increase output, all only through increasing labour
