Chapter 7

Costs and Cost Minimization

Introduction

The last chapter considered how to represent production in economic theory

This chapter presents cost concepts, and links the analysis of cost to the theory of production

Cost Concepts

Some Terminology: Opportunity Cost Implicit and Explicit Costs Sunk and Non-sunk Costs Fixed Costs and Variable Costs Long-run and Short-run Costs

Opportunity Cost

Opportunity Cost: The cost of using a resource is the value that resource would have produced in its best alternative activity. Opportunity cost is always the relevant concept

for use in economic decision-making. Opportunity cost includes implicit and explicit

costs. Explicit costs involve direct flows of money in a

transaction, implicit costs do not.

Sunk Costs

Sunk cost: If a cost has already been incurred and is irretrievable or irreversible, it is sunk. Sunk costs are irrelevant for current economic decisions. Whether a cost is sunk or not depends on the timing:

Before you build a factory, your investment is not sunk. However, after a factory is built, and if the factory has no

alternative uses or resale value, then the investment expenditure is sunk.

Fixed Costs and Variable Costs

A fixed cost is one that does not vary with output produced within a period

Variable costs do vary with output produced in a period

Fixed Costs and Sunk Costs

Fixed costs are not always sunk Example: You need a plane to run an air shuttle

service between two towns. Costs associated with the plane may be fixed, but

if the plane can be sold these costs are not sunk.

Long-run and Short-run

The long run is a time period in which all of a firm’s inputs can be varied

The short run is a time period in which the quantity of at least one input is considered fixed

Cost Minimization

We will assume that firms maximize profits, which will require that they minimize the cost of production of their chosen output

We examine cost minimization in the long run and in the short run

Cost Minimization: Long Run

Consider a firm that uses only two inputs, L and K, to produce output in a period.

Prices of the services of capital and labor for a period are w and r.

If the firm uses quantities L and K to produce output, its total costs are given by:

TC wL rK

Isocost Lines

Consider plotting combinations of inputs that are equally costly For example, let w = 5 and r = 10. What are all the bundles that would cost $100? $150?

200?

The resulting lines are isocost lines (these are very similar in construction to consumer budget lines)

What is the slope of an isocost line? Plot L on the horizontal axis and K on the vertical axis. Answer is w/r

A Diagram

Consider a diagram this problem for a firm: Minimize the cost of producing a given output, say Q = 20, using quantities of inputs, L and K, which have prices w and r. Plot the isoquant for Q = 20; plot a family of isocost

curves.

A Diagram

L

K

Q = 20

Find a point on the Q = 20 isoquant with the lowest production cost (on the isocost line with lowest cost).

Question

Does the preceding diagram illustrate the solution to a long-run or a short-run cost minimization problem? A: Short-run B: Long-run

Question

Does the preceding diagram illustrate the solution to a long-run or a short-run cost minimization problem? A: Short-run B: Long-run

The Tangency Condition

The solution to the cost minimization problem occurs at a point of tangency

This implies that the slope of the isoquant is equal to the slope of an isocost line

L

K

MP w

MP r

L KMP MP

w r

Question

Suppose: MPL = 5 MPK = 8 w = 10 r = 12

True or False? The firm should use more capital and less labor. A: True B: False

Question

Suppose: MPL = 5 MPK = 8 w = 10 r = 12

True or False? The firm should use more capital and less labor. A: True B: False

Derive the Long-run Total Cost Curve

Use the isoquant/isocost diagram For each possible output, find the cost minimizing

input combination, and the resulting level of total cost

Then plot Q versus TC using the “data” generated from the isoquant-isocost diagram. This is a long-run total cost curve.

A Diagram

L

K

Q = 20

Find a point on the Q = 20 isoquant with the lowest production cost (on the isocost line with lowest cost).

Q = 30

Q = 10

C = 100 C = 170 C = 300

Long-Run Total Cost Curve

10 20 30Q

C

100

200

300

Long-Run Total Cost Curve

10 20 30Q

C

100

200

300

Input Substitutability

Suppose that labor becomes more expensive. What happens to the cost-minimizing combination of inputs to produce a given output? If the wage rate rises, the capital/labor ratio rises. Show this in a diagram!

Recall the elasticity of substitution: What does this say about how changes in input

prices affect input combinations?

Cost Minimization: Short Run

In the short-run, at least one input quantity is “fixed” For example, over a short time horizon the size of

a factory may be fixed, but labor employed could vary.

If capital is fixed, then the costs associated with capital will also be fixed. For any positive output we must pay the fixed cost

associated with the capital input. If output is zero, this cost is avoidable if the cost is not

sunk.

Short-run Cost Minimization: Diagram

L

K

Q = 20

With capital fixed, find the amount of labor needed to produce a given output, then find the isocost through that point.

Q = 30

Q = 10

K1

Short-Run Total Cost Curve

10 20 30Q

C

100

200

300

I-clicker Question Which statement correctly describes the relationship

between long-run and short-run total costs? A: The long-run total cost of producing an given output (for

example, Q = 100) is always less than the short-run cost of producing the same output.

B: The long-run total cost of producing an given output (for example, Q = 100) is always less than or equal to the short-run cost of producing the same output.

C: The short-run total cost of producing an given output (for example, Q = 100) is always less than the long-run cost of producing the same output.

D: The short-run total cost of producing an given output (for example, Q = 100) is always less than or equal to the long-run cost of producing the same output.

I-clicker Question Which statement correctly describes the relationship

between long-run and short-run total costs? A: The long-run total cost of producing an given output (for

example, Q = 100) is always less than the short-run cost of producing the same output.

B: The long-run total cost of producing an given output (for example, Q = 100) is always less than or equal to the short-run cost of producing the same output.

C: The short-run total cost of producing an given output (for example, Q = 100) is always less than the long-run cost of producing the same output.

D: The short-run total cost of producing an given output (for example, Q = 100) is always less than or equal to the long-run cost of producing the same output.

The End