Handout 5: Theory of the Firm- Production; Cost Functions Flashcards
Production Function
How much output will be produced given a certain amount of labor and other inputs
Marginal Product of Labor
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.
Marginal Product of Capital
incremental increase in output one would obtain by adding an extra unit of capital, holding labor fixed.
Avg. Product of Labor
- ratio of total output to total labor used
- units of output per unit of labor
- APL = Q/L = f(K,L)/L
Avg. Product of Capital
- ratio of total output to total capital used
- units of output per unit of capital
- APK = Q/K = f(K,L)/K
Isoquants
- 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
Rate of Technical Substitution (RTS)
-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
Decreasing Returns to Scale (DRTS)
- 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
Constant Returns to Scale (CRTS)
- if increasing all inputs by the same proportion increases output by exactly the same proportion
- Cost functions are straight (upward-sloped) lines
Increasing Returns to Scale (IRTS)
- 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
Optimal Scale Production Functions
- 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
Isocost Line
Plots all combinations of K and L that, if used by the firm, will result in the same total cost.
TC = wL + rK
Cost Minimization
-slope of the isoquant equals the slope of the isocost
RTS = w/r
Derived Demands for L and K
-the demands for L and K we get from cost minimization
Expansion Path
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)
Total Cost functions
show how much it will cost to produce different levels of output given that the firm chooses its inputs to minimize costs
Long-run cost functions
how costs change with output given that ALL inputs can be altered
Short-run cost functions
-cost functions firms face given that one or more inputs is held fixed
Average Cost
measures the ratio of total cost to total output
Marginal Cost
incremental change in cost due to an incremental increase in output (so MC is the slope of a cost curve)
First and Second Welfare Theorems
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
