Question

In: Economics

Assume that U.S. can produce two goods, compact discs and apples. Compact discs are produced using...

Assume that U.S. can produce two goods, compact discs and apples. Compact discs are produced using capital and labor. Apples are produced using land and labor. The total supply of labor is 20 workers. Given the supply of capital, the marginal products of labors are as follows:

Number of Workers Employed

Marginal Product of Labor in Compact Disc Sector

Marginal Product of Labor

in Apples Sector

1

16

14

2

15

13

3

14

12

4

13

11

5

12

10

6

11

9

7

10

8

8

9

7

9

8

6

10

7

5

11

6

4

12

5

3

13

4

2

14

3

1

15

2

0

Suppose that the price of a compact disc is $2 and the price of apples is $1

The equilibrium allocation of labor between the compact disc sector (LCD) and the apple sector (LA) is respectively

a.

LCD = 11 and LA = 9
b.

LCD = 9 and LA = 11
c.

LCD = 10 and LA = 10
d.

LCD = 13 and LA = 7
e.

LCD = 14 and LA = 6

B)

Suppose that the price of a compact disc is $2 and the price of apples is $1

The equilibrium wage rate (w) is

a.

w = $6
b.

w = $7
c.

w = $8
d.

w = $9
e.

w = $10

Solutions

Expert Solution

(A) Given, the price of a compact disc is $2 and the price of apples is $1

Thus Marginal Revenue Product (MRP) of Labor in Compact Disc Sector and Marginal Revenue Product (MRP) of Labor in Apples Sector for an additional labour is equal Marginal Product times price. The calculations are shown in the following table.

Number of Workers Employed Marginal Product of Labor in Compact Disc Sector Marginal Product of Labor in Apples Sector MRP (Compact Disc Sector) MRP (Apples Sector)
1 16 14 32 14
2 15 13 30 13
3 14 12 28 12
4 13 11 26 11
5 12 10 24 10
6 11 9 22 9
7 10 8 20 8
8 9 7 18 7
9 8 6 16 6
10 7 5 14 5
11 6 4 12 4
12 5 3 10 3
13 4 2 8 2
14 3 1 6 1
15 2 0 4 0

Now, the equilibrium allocation of labor between the compact disc sector (LCD) and the apple sector (LA) is respectively LCD=13 and LA=7 beacuse the total supply of labor is 20 and equilibrium allocation of labor is satisfied with wage $8 (i.e. MRP=wage=$8).

Hence the option d is the correct answer.

B) Now if the price of a compact disc is $2 and the price of apples is $1 remain same as above case then the equilibrium wage rate (w) is $8.

Thus the option c is the correct answer.

Rahul Sunny answered 7 months ago
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