1
3 0 6 - 3 1 0
E N G I N E E R I N G
E C O N O M Y
SOLUTIONS TO PROBLEM SET #4 – PRODUCTION AND COST ANALYSES
1.
i)
The total cost function consists of two linear segments intersecting at a rate of 500 units
per week.
Let L represent the number of person-hours of labour employed per week.
The mar-
ginal cost function is:
For L
≤
500:
MC = 20
(also vc because of the linear cost function)
For L 500:
MC = 30
At the current production rate, the total production costs are:
400 (50) = 20 000
Therefore, the fixed cost is:
20 000 - 400 (20) = 12 000
The total production cost function is:
For L
≤
500:
TC = 12 000 + 20 (L)
For L 500:
TC = 12 000 + 20 (500) + 30 (L - 500) = 7000 + 30 L
Therefore, the average cost function is:
For L
≤
500: AC = 12 000 / L + 20
For L 500:
AC = 7000 / L + 30
The marginal and average cost curves are shown in the diagram below.
0
20
40
60
80
100
120
140
160
180
200
0
100
200
300
400
500
600
700
800
900
1000
PRODUCTION RATE
(units/week)
UNIT COSTS
($)
Average Cost
Marginal Cost

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