4a. Short-run Costs and Production

Question 1

What is the TC equation?

Answer 1

TC = VC(q) + FC

Question 2

What is “total cost”?

Answer 2

the sum of a firm’s variable cost and fixed cost

Question 3

What is specific about “variable cost” in the short run?

Answer 3

remember, in the SHORT RUN, only variable cost changes, hence MC must be marginal variable cost

Question 4

What is “marginal cost”?

Answer 4

Marginal cost (MC) – the amount by which a firm’s cost changes if the firm produces one more unit of output.

Question 5

What is the equation of “marginal cost”?

Answer 5

Question 6

How are Marginal Cost and Marginal Product related in the short-run?

Answer 6

If a firm in the SR cannot vary capital, the only way to increase output is by using more labor.

The extra labor required to produce one more unit of output is (delta L / delta Q). The EXTRA labor costs the firm w per unit, so the firm’s cost RISES
by w(delta L / delta Q)…
HOWEVER, we can flip (delta L / delta Q) to (delta Q / delta L) which IS MPL (the additional output per extra unit of labor),
however, as we flipped we now have to divide w by MPL, hence forming that equation

Question 7

What does an MPL of 3 say about Q and L?

Answer 7

1 unit of L = 3 units of output

Question 8

What is the equation to calculate MC using MPL (in the SR)?

Answer 8

MC = w / MPL

Question 9

What is the equation to calculate AVC using MPL (in the SR)?

Answer 9

AVC = w / MPL

Question 10

What do we assume about fixed costs in the long run?

Answer 10

Fixed costs are avoidable in the long run.
Hence why.. we assume that all inputs can be varied in the long run so that the firm has no long-run fixed costs (F = 0).
-> As a result, the long-run total cost equals: C=VC

Question 11

What is the long run total cost equal to?

Answer 11

C = VC
Variable cost!!

-> Because we assume that all inputs can be varied in the long run so that the firm has no long-run fixed costs (F = 0).

Question 12

What is the long run cost equation of the firm?

Answer 12

w = wage
r = rental rate

Question 13

What is challenging about cost minimization in the long run?

Answer 13

Short Run problem: choose L to produce q and maximize profit

But in the long run…
choose how to combine L and K to produce q and maximize profit
–> Different combinations of L and K to produce a given q (isoquant) have different costs!
–> To maximize profit, the firm must choose the cheapest combination of L and K that allow to produce q.
-> Along an isocost line, cost is fixed at a particular level, C, so by setting cost at C (BASICALLY LIKE AN ISOQUANT)

Question 14

What is the mathematical expression of cost minimization in the long run?

Answer 14

mathematical expression:
-> row 1: choose the value of L and K that make the equation (wL + rK) the minimum
-> row 2: provided that L and K PRODUCES the quantity of output Q i desire

Question 15

What two curves are required for cost minimization?

Answer 15

You need two ingredients, isocosts and isoquants

Question 16

What is an “isocost” line?

Answer 16

Isocost Line:
Expenditure when firm buys L and K
-> Expenditure = wL + rK
-> Fix the expenditure and find all combination of L and K that firm can buy in the market spending the same.
-> In terms of K? Re-write

Question 17

What is the equation of the isocost line?

Answer 17

Question 18

What is important to remember about the slopes of isocost lines?

Answer 18

Always the SAME slope
-> The slope shows the rate at which the firm can substitute capital for labor holding total cost constant

Question 19

What are the 3 justifications for cost minimizations?

Answer 19

Lowest-isocost rule

Tangency rule

Last-dollar rule

Question 20

What is the “lowest-isocost rule”?

Answer 20

Pick the bundle of inputs where the lowest isocost line touches the isoquant.

Question 21

What is the “tangency rule”?

Answer 21

Pick the bundle of inputs where the isoquant is tangent to the isocost line.

Question 22

What is the “last-dollar rule”?

Answer 22

Pick the bundle of inputs where the last dollar spent on one input gives as much extra output as the last dollar spent on any other input.

Question 23

Using all the rules, justify which point minimizes cost?

Answer 23

Point x is the answer

Lowest-Isocost rule:
the $2k isocost is the lowest isocost that TOUCHES the isoquant

Tangency rule:
at point x, the slope of the isocost is the same as MRTS, slope of the isoquant

Last-dollar rule:
at point x, the last dollar spent on labor adds as much extra output as the last dollar spent on capital

Question 24

Using the “last dollar rule”, explain point y does not minimize costs

Answer 24

-> spending 1 extra dollar on capital would result in “only” an additional 0.017 units of output
-> on the other hand… spending 1 extra dollar on labour would result in an additional 0.1 units of output
-> hence why y is cost-inefficient

Question 25

What happens to an isocost if a factor (r or w) changes in price?D

Answer 25

In this example the wage falls from $24 to $8 but the rental rate of capital stays constant at $8.

Because of the wage decrease, the new isocost lines have a flatter slope, -w/r = -8/8 = -1, than the original isocost lines, -w/r = -24/8 = -3.

The new, flatter isocost line is tangent to the isoquant at Bundle v

Thus, the firm uses more labor and less capital as labor becomes relatively less expensive. Moreover, the firm’s cost of producing 100 units falls from $2,000 to $1,032 because of the decrease in the wage.

Question 26

What is the “long run expansion path”?

Answer 26

As a firm increases output, the expansion path traces out the cost-minimizing combinations of inputs employed to produce each possible level of output q.

Question 27

Why is the LRAC curve U shaped?

Answer 27

Shape is due to economies and diseconomies of scale.

Question 28

The LRAC is the _________ of the SRACs

Answer 28

The LRAC is the envelope of the SRACs

Question 29

Why must SRACs always be greater than the LRAC?

Answer 29

eg. want to produce quantity 2.. if you are using the wrong quantity of capital in the short run (which you thus cant vary) in SRAC1, you will have a much higher average cost of price d. Whereas in the long run you can choose the optimal quantity of capital which allows you to produce q2 at a price of point e.

In the long run, the firm chooses the plant size that minimizes its cost of production, so it picks the plant size that has the lowest average cost for each possible output level. At q1, it opts for the small plant size, whereas at q2, it uses the medium plant size. Thus, the long-run average cost curve is the blue-green, scalloped section of the three short-run cost curves.

Question 30

What is the difference between short-run and long-run expansion paths?

Answer 30

In the short run, the firm cannot vary its capital, so its short-run expansion path is horizontal at the fixed level of capital

In the long run, the manufacturer increases its output by using more of BOTH inputs, so its long-run expansion path is upward sloping

This also confirms the LRAC “envelope”, as the long-run expansion path is hence always lower or equal to the short-run

Question 31

What is “learning by doing”?

Answer 31

“the productive skills and knowledge that workers and managers gain from experience. “

Question 32

Can a firm control the price?

Answer 32

It depends on the market structure.

Question 33

What is key about “perfect competition”?

Answer 33

Perfect competition: buyers and sellers have no power over the price. They are PRICE TAKERS

• A firm is unable to sell its output at a price greater than market price. A consumer is unable to purchase at a price less than the market price.
• This is what most people mean when they talk about “competitive firms.”

Large number of firms, Identical (homogeneous) products, consumers have full information, free entry and exit

Question 34

What price control do firms have in “perfect competition”?

Answer 34

NONE.

They take the price of the market