Activity Name: A firm has two factories with different marginal costs of product
ID: 1134206 • Letter: A
Question
Activity Name: A firm has two factories with different marginal costs of production as given below Marginal cost for factory 1 Marginal cost for factory 2 MC-20+80, MC -60+4Q2 The firm wants to produce a total of 200 units of output (Q) Suppose the firm produces 100 units at each factory. In this case The marginal cost of producing the 100 unit at factory 1 is The marginal cost of producing the 100 unit at factory 2 is The total cost of producing the 100 units at factory 1 is The total cost of producing the 100 units at factory 2 is A better strategy would be to produce more/less at factory 1 and more/less at factory 2. In this case How much will be produced at factory 1? How much will be produced at factory 2? What is the total cost at factory 1? What is the total cost at factory 2?Explanation / Answer
The formula for TC1 is integration of MC1=20+8Q
TC1=20Q+4Q^2
The formula for TC2 is integration of MC2=60Q+4Q
TC2 =60Q+2Q^2
Q1
MC1
TC1
Q2
MC2
TC2
100
820
42000
100
460
26000
MC1 of 100th unit at factory 1 is $820
MC2 of 100th unit at factory 2 is $460
The TC1 of 100 units at factory 1 is $42000
The TC2 of 100 units at factory 2 is $26000
A better strategy would be to produce less at factory 1 and more at factory 2
Factory 1 would produce 40 units
Factory 2 would produce 60 units
TC at factory 1 is $7200
TC at factory 2 is $10800
Q1
MC1
TC1
Q2
MC2
TC2
TC
0
20
0
100
460
26000
26000
10
100
600
90
420
21600
22200
20
180
2000
80
380
17600
19600
30
260
4200
70
340
14000
18200
40
340
7200
60
300
10800
18000
50
420
11000
50
260
8000
19000
60
500
15600
40
220
5600
21200
70
580
21000
30
180
3600
24600
80
660
27200
20
140
2000
29200
90
740
34200
10
100
800
35000
100
820
42000
0
60
0
42000
Q1
MC1
TC1
Q2
MC2
TC2
100
820
42000
100
460
26000
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