Review Notes – Production, Technology and Profit Maximization

The shape of the isoprofit curves depends on the shapes of and the AC curve In the case of Apple Cinnamon Cheerios this is particularly simple AC is a horizontal line and the equation of the isoprofit curves is So the isoprofit curves are decreasing and convex, like , as we see in Figure 1

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Review Notes – Production, Technology and Profit Maximization

• What does the isoprofit look like graphically? • How many isoprofit curves are there? • What is its slope and intercept? • What is the slope of the production function in the short – run? • Maximizing profit requires that the isoprofit be tangent to the production function Why? • In other words => MPL = w/P

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• An isoprofit curvegives all the risk-wage combinations that yield the same level of profits to a firm • Isoprofit curves are upward sloping because production of safety is costly • Wage-risk combinations on higher isoprofit curves yield lower profits A wage cut shifts the isoprofit curve down

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The slope of an isoprofit line depends on the ratio of the x good’s profit-per-unit to y good’s profit-per-unit The profit amount for the isoprofit line that just touches the feasible area is the most profit you can make The X and Y coordinates of the point where the isoprofit line touches tells you how much of x and y to make

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•Definition Cut cis stronger than cut c’if zLP< zLP’, where LP includes c and LP’ includes c’ isoprofit fractional solution stronger cuts Cut strength 10 •Step 1: Solve LPR Get x* •Step 2: If x*integral, stop Else, find a valid inequality that excludes x*(a “cut”) •Step 3: Go to Step 1 èkeep strengthening the formulation

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Review Notes - Production, Technology and Profit Maximization

The Production Function.

Y = f(L, K, N, E) - what does this mean?

Graphically

What is the production set?

Isoquants

Definition given Y

= f(L, K): Shows all combinations of L and K that give output Y

What are some examples of isoquants?

Assumptions about production

Free Disposal or Monotonic Technology

Convexity of isoquants

Why do these assumptions make sense?

Other Definitions

Marginal Product of the any input equals?

Technical Rate of Substitution? Slope of the isoquant curve and equals what?

Short- run vs. Long-run in production

Returns to Scale

Constant Returns to Scale

Decreasing Returns to Scale

Increasing Returns to Scale

What is the difference between returns to scale and diminishing returns?

Profit Maximization

Definitions

Total Revenue

Total Costs

Which costs are included?

Profit

Economic profit vs. accounting profit

Types of Inputs

Variable inputs

Fixed inputs

Quasi-fixed inputs

Short-run profit maximization

Assume 2 inputs, one variable (L) and one fixed (K) Firm problem is to max profit (ʌ) subject to Y = f(L, K) with K fixed

ʌ = Pf(L,K) - wL - rK

What is an isoprofit curve?

Y = ʌ/P + wL/P + rK/P

What does the isoprofit look like graphically?

How many isoprofit curves are there?

What is its slope and intercept?

What is the slope of the production function in the short - run? Maximizing profit requires that the isoprofit be tangent to the production function. Why?

In other words => MP

L = w/P

What happens to input usage when P, L, MP

L change in the short-run?

Graphically? Mathematically?

Long-run profit maximization

Maximizing profit requires that the isoprofit be tangent to the production function for both inputs. Why?

In other words both

MP L = w/P MP K = r/P Or MP L /w = MP K /r

Or w/MP

L = r/MP K Make sure you know how to interpret both conditions, how they work, how they are similar, how they are different. L = f(P,w,r); K = f(P,w,r) are the factor demand curves. What are these?

[PDF] Review Notes – Production, Technology and Profit Maximization