Industrial Location

Chapter 4

Three Isoquants

Isocost curve

Slope of isoquant

• For a production function with two inputs,

• Along an isoquant, the change in output is zero, so

• Therefore,

xMPxxMPxOutput 2121

xMPxxMPx 2121

0

MPX

MPXX

X

1

2

2

1

Equilibrium for a Firm

• Slope of Isoquant = Slope of Isocost

orPx

PxMPx

MPx

1

2

1

2

Px

MPxPx

MPx

2

2

1

1

Isocost curve and isoquant map showing a firm’s equilibrium

Resource use based on location

Pine Grove vs Urban Center

Pine GrovePine Grove• Boughs:$150 per load• Wages:$400 / week

Urban CenterUrban Center • Boughs:$250 per load• Wages:$200 / week

,400$150$ LaborPineTC

,67.2150$

or ,150$

400$

150$

LaborTC

Pine

LaborTC

Pine

,200$250$ LaborPineTC

.80.0250$

or ,250$

200$

250$

LaborTC

Pine

LaborTC

Pine

Three isocost curves for $1,000, $2,000, and $3,000

Pine GrovePine Grove• For $1,000, the firm makes 300

wreaths per week, and • Uses 5.253 loads of pine and 0.53

units of laborTC = $1,000 = ($150  5.253) + 

($400  0.53). • For $2,000, the firm makes 800

wreaths per week, and• Uses 8 loads of pine and 2 units

of labor TC = 2,000 = ($150  8) +

($400  2)

Urban CenterUrban Center• For $2,000 the firm makes 800

wreaths per week, and • Uses 4.4 loads of pine and 4.5

units of labor TC = $2,000 = ($250  4.4) +($200  4.5).

• For $3,000, the firm makes 1,500 wreaths per week, and

• Uses 5.6 loads of pine and 8 full-time workers.TC = $3,000 = ($250  5.6) +

($200  8).

Long–run average cost curve

Location orientation chart

Long–haul economies

Table 4–1. Hypothetical Transportation Costs

Distance from the

input source

Distance from the market to

inputs source

Column A cost of

procuring inputs

Column B cost of

distributing output

Column Ctotal transport

costs (A + B)

0 10 4.00 6.00 10.00

1 9 4.48 5.95 10.43

2 8 4.92 5.80 10.72

3 7 5.32 5.55 10.87

4 6 5.68 5.20 10.88

5 5 6.00 4.75 10.75

6 4 6.28 4.20 10.48

7 3 6.52 3.55 10.07

8 2 6.72 2.80 9.52

9 1 6.88 1.95 8.83

10 0 7.00 1.00 8.00

Total Transport Costs

Table 4–2. Calculation of Ideal Weights for Two Inputs and an Output

Input A Input B Output

Transport cost per ton per mile 30¢ 20¢ 50¢

Number of tons per week 30 50 10

Ideal weight 9 10 5

Firm location on non–linear routes