Production & Costs Continued… Agenda: I.Consumer and Producer Theory: similarities and differences II. Isoquants & The Marginal Rate of Technical Substitution.

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Presentation transcript:

Production & Costs Continued… Agenda: I.Consumer and Producer Theory: similarities and differences II. Isoquants & The Marginal Rate of Technical Substitution III. Diminishing vs. Decreasing Returns IV. Isocosts V. Putting it together: Optimal Production & Examples

Indifference curves Utility curves Budget constraint Different notation Same meaning! Consumer Utility Maximization

The Production Mountain Quantity per unit of labor holding capital constant Quantity per unit of capital holding labor constant Isoquants: Combinations of capital and labor that produce a given quantity Long Term we can vary both capital and labor

The Marginal Rate of Technical Substitution If we change the amount of capital we use, how much do we need to change the amount of labor to make the same quantity? Airplane Game Isoquants Isoquants paper labor 1 X Y 1 1

Isoquants vs. Indifference Curves IsoquantsIndifference Curves Convexity from diminishing marginal rate of technical substitution More is better Quantity is a cardinal measure Can only change both capital and labor in the long run. Convexity from preference assumption More is better Utility is an ordinal measure Individuals make trade-offs both at one time and over time

Diminishing vs. Decreasing returns All Isoquants are convex and slope down: diminishing MRTS Quantity increases at a decreasing rate as all inputs increase: decreasing returns

Isocost Lines What is an equation to represent the total cost of production? C=P K K + P L L Can we re-arrange this to fit the equation for a line in (L,K) space?

What is the optimal input combination GIVEN cost or quantity? “No matter what the structure of industry may be… (for profit or not for profit) … the objective of most producers is to produce any given level and quality of output at the lowest possible cost. Equivalently, the producer wants to produce as much output as possible from a given expenditure on inputs.” (Frank p. 233) Maximize Q given C Minimize C given Q r = cost of capital w = cost of labor Marginal products per dollar Duality

Example: If the MRTS between capital and labor is 1/2, the interest rate is 5% (use 5) and the wage rate is $10 per hour, is the firm maximizing production? How should the firm adjust its mix of capital and labor? 2 1/2 The firm is spending more than it has to!Use LESS labor, MORE capital The firm could be making more for the same cost!

Example: If the marginal product of labor is 5 and the marginal product of capital is 2, the price of labor is $20 and the cost of capital is 4%, is the firm optimizing production? To increase the marginal product of labor, reduce labor. To decrease the marginal product of capital, increase capital. You can NOT control interest rates or reduce wages in perfect capital or labor markets. (that said… change term structure, reduce benefits, training, perks…)