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Production & Costs Continued…

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

darius-farrell
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Production & Costs Continued…

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  1. Production & Costs Continued… • Agenda: • 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

  2. Consumer Utility Maximization Indifference curves Budgetconstraint Utility curves Different notation Same meaning!

  3. 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

  4. paper Y X 1 1 labor 1 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? Isoquants Airplane Game Isoquants

  5. Isoquants vs. Indifference Curves Isoquants Indifference 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

  6. 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 +20 +40 +60 +60 +60 +90 +60

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

  8. 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) Duality w = cost of labor Maximize Q given C Minimize C given Q r = cost of capital Marginal products per dollar

  9. 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? The firm could be making more for the same cost! Use LESS labor, MORE capital The firm is spending more than it has to! 2 1/2

  10. 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…)

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