Question

4. Suppose that your production function is q(L) = 10412 a. In a table, calculate the output, average product and marginal product for L = 1, 2, 3, ..., b. Suppose fixed costs are $100 and the price of labor is $20. In a table, calculate the average cost and marginal cost for L = 1, 2, 3, ... , 9. c. If you could sell your output for $9, how many workers would you hire?

Need help solving and explaining how to get to that answer.

Answer 1

We have the following information

Production function: q(L) = 10L^1/2

Labor (L)	Output	Average Product	Marginal Product
1	10.0	10.0	--
2	14.1	7.1	4.1
3	17.3	5.8	3.2
4	20.0	5.0	2.7
5	22.4	4.5	2.4
6	24.5	4.1	2.1
7	26.5	3.8	2.0
8	28.3	3.5	1.8
9	30.0	3.3	1.7

Average product (AP) of labor is total output divided by the total quantity of labor. Marginal product (MP) of labor is change in total output as the labor unit is increased by one.

It is given that the fixed cost is $100. Moreover, the price of labor is $20 which can be taken as the variable cost as well as the wage rate

Labor (L)	Fixed Cost ($)	Variable Cost ($)	Total Cost ($)	Marginal Cost ($)
1	100	20	120	--
2	100	40	140	20
3	100	60	160	20
4	100	80	180	20
5	100	100	200	20
6	100	120	220	20
7	100	140	240	20
8	100	160	260	20
9	100	180	280	20

The equilibrium level of labor can be attained by equating the wage rate ($20) with the value of marginal product (VMP) of labor which marginal product of labor multiplied by the price of the output ($9)

Labor (L)	Output	Average Product	Marginal Product	Fixed Cost ($)	Variable Cost ($)	Total Cost ($)	Marginal Cost ($)/Wage Rate	Price ($)	VMP
1	10.0	10.0	--	100	20	120	--	9	--
2	14.1	7.1	4.1	100	40	140	20	9	37
3	17.3	5.8	3.2	100	60	160	20	9	29
4	20.0	5.0	2.7	100	80	180	20	9	24
5	22.4	4.5	2.4	100	100	200	20	9	21
6	24.5	4.1	2.1	100	120	220	20	9	19
7	26.5	3.8	2.0	100	140	240	20	9	18
8	28.3	3.5	1.8	100	160	260	20	9	16
9	30.0	3.3	1.7	100	180	280	20	9	15

From the table above one can see that the equilibrium level of labor is 5 units.