Handout 5: Theory of the Firm- Production; Cost Functions

Question 1

Production Function

Answer 1

How much output will be produced given a certain amount of labor and other inputs

Question 2

Marginal Product of Labor

Answer 2

the incremental increase in output one would obtain by adding an extra unit of labor, holding capital fixed

• positive at low levels of labor, may increase as more labor is added at low levels of labor.
• eventually declines as more of one input is added, holding other input fixed
• at high enough levels of an input, marginal products may become negative. For example, if you add too many workers to a single machine, they get in each other’s way and actually reduce output.

Question 3

Marginal Product of Capital

Answer 3

incremental increase in output one would obtain by adding an extra unit of capital, holding labor fixed.

Question 4

Avg. Product of Labor

Answer 4

• ratio of total output to total labor used
• units of output per unit of labor
• APL = Q/L = f(K,L)/L

Question 5

Avg. Product of Capital

Answer 5

• ratio of total output to total capital used
• units of output per unit of capital
• APK = Q/K = f(K,L)/K

Question 6

Isoquants

Answer 6

• shows all combinations of K and L that will yield the same level of output
• similar to an individual’s indifference curve but instead of showing utility it shows output quantity

Question 7

Rate of Technical Substitution (RTS)

Answer 7

-negative of the slope of an isoquant
-measures the tradeoff firms can make between two inputs, holding output fixed
-similar conceptually to marginal rate of substitution (MRS) but instead of measuring tradeoff between two products, holding utility fixed, tradeoff between inputs holding output fixed
-declines as one moves along an isoquant
-RTS is equal to the ratio of the marginal product of labor to the marginal product of capital
RTS (L for K) = MPL/MPK

Question 8

Decreasing Returns to Scale (DRTS)

Answer 8

• if increasing all inputs by the same proportion increases output by less than that proportion
• cost functions increase at an increasing rate. Doubling output requires more than a doubling of inputs, so costs more than double.
• Avg. cost increases with output

Question 9

Constant Returns to Scale (CRTS)

Answer 9

• if increasing all inputs by the same proportion increases output by exactly the same proportion
• Cost functions are straight (upward-sloped) lines

Question 10

Increasing Returns to Scale (IRTS)

Answer 10

• if increasing all inputs by same proportion increases output by more than that proportion.
• Cost functions increase at a decreasing rate. Doubling output requires less than a doubling of inputs, so costs less than double.
• Avg. cost declines with output levels

Question 11

Optimal Scale Production Functions

Answer 11

• at low levels of output, firms display increasing returns to scale, at very high levels of output, decreasing returns to scale set in.
• MC and AC will first decline and then rise

Question 12

Isocost Line

Answer 12

Plots all combinations of K and L that, if used by the firm, will result in the same total cost.
TC = wL + rK

Question 13

Cost Minimization

Answer 13

-slope of the isoquant equals the slope of the isocost

RTS = w/r

Question 14

Derived Demands for L and K

Answer 14

-the demands for L and K we get from cost minimization

Question 15

Expansion Path

Answer 15

the set of cost-minimizing input combos a firm will choose to produce various levels of output (when the prices of inputs are held constant)

Question 16

Total Cost functions

Answer 16

show how much it will cost to produce different levels of output given that the firm chooses its inputs to minimize costs

Question 17

Long-run cost functions

Answer 17

how costs change with output given that ALL inputs can be altered

Question 18

Short-run cost functions

Answer 18

-cost functions firms face given that one or more inputs is held fixed

Question 19

Average Cost

Answer 19

measures the ratio of total cost to total output

Question 20

Marginal Cost

Answer 20

incremental change in cost due to an incremental increase in output (so MC is the slope of a cost curve)

Question 21

First and Second Welfare Theorems

Answer 21

First theorem of welfare economics: A perfectly competitive equilibrium will
bring about an e¢ cient allocation of resources (pareto optimal).
Second theorem of welfare economics: Any e¢ cient allocation can be achieved by
a competitive equilibrium (after a suitable redistribution of initial endowments).
While all competitive equilibria lead to an e¢ cient allocation (1st), not all e¢ -
cient allocations are equilibria. However, any e¢ cient allocation can be attained
as a competitive equilibrium, if necessary, after a suitable redistribution of endowments