Question

Consider an economy that can produce two goods, manufactures and food. Manufactures are produced using capital and labor. Food is produced using land and labor. The total supply of labor is 20 units. Given the supply of capital and land, the marginal products of labors are as follows:

Marginal Product of Labor in Manufacturing Sector Marginal Product of Labor in Food Sector Number of Workers Employed 20 1 16 2 15 19 3 14 18 13 4 17 12 5 16 6 11 15 7 10 14 13 9 12 10 7 11 11 6 10

Suppose that the price of manufactures is 2 and the price of food is 1.

A.Determine graphically and algebraically the wage rate and the allocation of labor between the two sectors

B.Calculate, using geometric techniques, the income of capitalists, the income of landowners, and the income of workers in each sector.

Answer 1

In an economy, the total labor supply is 20 units. Two goods are being produced, manufacturers and foods. Food is using land and labor. While manufacturers is using capital and labor. The price of manufacturers is 2 and the price of food is 1.

The following table shows the marginal product of labor in the two sectors.

Number of workers	Marginal product in manufacturers	Marginal product in the food	Marginal revenue product in manufacturers	Marginal revenue product in the food
1	16	20	32	20
2	15	19	30	19
3	14	18	28	18
4	13	17	26	17
5	12	16	24	16
6	11	15	22	15
7	10	14	20	14
8	9	13	18	13
9	8	12	16	12
10	7	11	14	11
11	6	10	12	10
12	5	9	10	9
13	4	8	8	8
14	3	7	6	7
15	2	6	4	6
16	1	5	2	5
17	0	4	0	4

A. The marginal revenue product is the value produced by a labor. It is calculated as a marginal product of labor times the price of the product.

A 32 Workers in manufacturers 20 Workers in food E S T в 20 Of 13 17 Om Workers wages MRP CO wages/MRP

The equilibrium wage will be equal to the marginal revenue product of the workers and the equilibrium quantity of workers will be at the point where marginal revenue product will be equal for both the workers.
So, the equilibrium wage is 8 and the equilibrium quantity of workers for manufacturing is 13 units.

The equilibrium quantity of workers for food is 20-13 = 7 units.

B. Now, the triangular area under the marginal revenue product curve of workers in manufacturers sector will give the total income of capitalists.

We can find the total income of the capitalists by finding the area of the triangle.

Area ΔΑES x SEx AS =x 13x (32-8) 2 =156

So, the income of the capitalists is 156.

Now, the triangular area under the marginal revenue product curve of workers in foods sector will give the total income of landowners.

We can find the total income of the landowners by finding the area of the triangle.

Area ACET 1 x ETx CT 1 x (20-13) x (20-8) 2 = 42

So, the income of the landowners is 42.

The rectangular area under the marginal revenue product curve of workers in the manufacturer's sector will give the total income of workers in that sector.

We can find the total income of the workers in that sector by finding the area of the rectangle.

Area OMSEU = OmSx OmU X 8x13 -104

So, the income of the workers in the sector of the manufacturers is 104.

The rectangular area under the marginal revenue product curve of workers in the food sector will give the total income of workers in that sector.

We can find the total income of the workers in that sector by finding the area of the rectangle.

Area OFTEU =OfTxOfU X = 8x7 -56

So, the income of the workers in the food sector is 56