1 industrial location chapter 4. 2 three isoquants
TRANSCRIPT
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
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).
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
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