Question

4. Suppose that your production function is q(L) = 10L^1/2

a. In a table, calculate the output, average product and marginal product for L = 1,2,3,4,5,6,7,8,9.

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 = 1,2,3,4,5,6,7,8,9.

c. If you could sell your output for $9 how many workers would you hire?

Explain all answers

Answer 1

q = 10L^1/2

(a) AP = q/L = (10L^1/2)/L = 10L^-1/2

MP = dq/dL = 1/2(10)L^-1/2 = 5L^-1/2

(b) Fixed cost = $100

w = $20

TC = FC+ wL

AC= TC/q

MC = (Change in TC/Change in q)

L	q	AP=q/L	MP= (Change in TP/Change in L)	VMPL=(P)(MPL)=($9)(MPL)	TC= FC+wL	AC=TC/q	MC= (Change in TC/Change in q)
1	10	10	5	45	120	12	-
2	14.14	7.07	3.54	31.86	140	9.90	4.83
3	17.32	5.77	2.89	26.01	160	9.24	6.29
4	20	5	2.5	22.5	180	9	7.46
5	22.36	4.47	2.24	20.16	200	8.94	8.47
6	24.49	4.08	2.04	18.36	220	8.98	9.38
7	26.46	3.78	1.89	17.01	240	9.07	10.15
8	28.28	3.53	1.77	15.93	260	9.19	10.98
9	30	3.33	1.67	15.03	280	9.33	11.63

(c) P= $9

Optimal labor input is where VMPL = wage.

Value of marginal product of labor , VMPL = (P)(MPL)

We can see that when L=5 , VMPL >Wage

and when L=6 , VMPL<Wage.

Therefore, if price =$9 , then the firm would hire 5 workers.