Section 6

Costs

Intermediate Microeconomics

Section 6

Intermediate Microeconomics () Costs Section 6 1 / 22

Costs in the Short-Run

Costs

FC = rK0

VC = wL1

TC = rK0 + wL1

Intermediate Microeconomics () Costs Section 6 2 / 22

Costs in the Short-Run

The Relationship Between TP and TC

Intermediate Microeconomics () Costs Section 6 3 / 22

Costs in the Short-Run

Other Short-Run Costs

AFCQ1 =FC

Q1=

rK0

Q1

AVCQ1 =VCQ1

Q1=

wL1

Q1

ATCQ1 =(rK0 + wL1)

Q1

MCQ1 =∆TCQ1

∆Q1=

∆VCQ1

∆Q1=

w∆L1

∆Q1

Intermediate Microeconomics () Costs Section 6 4 / 22

Costs in the Short-Run

Graphing Short-Run Costs

Intermediate Microeconomics () Costs Section 6 5 / 22

Allocating Between Production Processes

MCA = 12QA ATCA =16

QA+ 6QA

MCB = 4QB ATCB =240

QB+ 2QB

What is the least costly way to produce 32 units?

Intermediate Microeconomics () Costs Section 6 6 / 22

Allocating Between Production Processes

An Example

Minimum cost⇒MCAQA

= MCBQB

equating MC: 12QA = 4QB

must produce 32 units total: QB = 32− QA

substituting into MC condition: 12QA = 128− 4QA

QA = 8

Intermediate Microeconomics () Costs Section 6 7 / 22

Relationship Between MP, AP, MC, and AVC

MC =w

MPAVC =

w

AP

Intermediate Microeconomics () Costs Section 6 8 / 22

Costs in the Long Run

TC = wL + rK

Intermediate Microeconomics () Costs Section 6 9 / 22

Costs in the Long Run

Cost Minimization

MPL

MPK=

w

r

MPL

w=

MPK

r

Intermediate Microeconomics () Costs Section 6 10 / 22

Costs in the Long Run

Why Do Unions Support Minimum Wages?

Intermediate Microeconomics () Costs Section 6 11 / 22

Costs in the Long-Run

Expansion Path

The locus of tangencies traced out by an isocost line of given slope as it shifts outwardsinto the isoquant map for a production process.

Intermediate Microeconomics () Costs Section 6 12 / 22

Costs in the Long-Run

Expansion Path

Intermediate Microeconomics () Costs Section 6 13 / 22

Costs in the Long-Run

From Expansion Path to Total Cost

Intermediate Microeconomics () Costs Section 6 14 / 22

Costs in the Long-Run

Other Long-Run Costs

LMCQ =∆LTCQ

∆Q

LACQ =LTCQ

Q

Intermediate Microeconomics () Costs Section 6 15 / 22

Costs and Returns to Scale

Constant Returns to Scale

Intermediate Microeconomics () Costs Section 6 16 / 22

Costs and Returns to Scale

Decreasing Returns to Scale

Intermediate Microeconomics () Costs Section 6 17 / 22

Costs and Returns to Scale

Increasing Returns to Scale

Intermediate Microeconomics () Costs Section 6 18 / 22

Returns to Scale and Industry Structure

Concentrated Industries

Intermediate Microeconomics () Costs Section 6 19 / 22

Returns to Scale and Industry Structure

Unconcentrated Industries

Intermediate Microeconomics () Costs Section 6 20 / 22

Long-Run v. Short-Run Costs

Intermediate Microeconomics () Costs Section 6 21 / 22

In-Class Questions

1 Sketch the TC, VC, FC, ATC, AVC, AFC, and MC curves for the productionfunction Q=3KL where K=2, r=3, and w=2.

2 A firm has access to two production processes:

MC1 = .4Q MC2 = 2 + .2Q

1 If it wants to produce 8 units of output, how much should it produce with with eachprocess?

2 If it wants to produce 4 units of output?

3 A firm has a production function Q = f (K , L) with constant returns to scale. Inputprices are r=3 and w=2. The output expansion path for this production function atthese input prices is a straight line through the origin. When it produces 5 units ofoutput, it uses 2 units of K and 3 units of L. How much K and L will it use when itslong-run total cost is equal to 120.

Intermediate Microeconomics () Costs Section 6 22 / 22