Answer to Question #92562 in Microeconomics for Huan LB

Question #92562
A firm has the following short-run production function: Q = 30L-2L2
a. Show the range of labor when stages I, II, and III of production occur.
b. If labor costs $20 per day, and the average price of service is $10, how many workers should the firm hire?
1
Expert's answer
2019-08-13T08:54:37-0400

a) Stage I - Between L= 0 and L where AP is maximized 

AP= " \\frac{Q}{L} "= " \\frac{30}{L} " - "\\frac{2L2}{L} " = 30-2L

" \\frac{dAP}{dL} "= 30 – 2L = 0 ⇒ L = "\\frac{30}{2} " = 15

Stage I from 0 to 15

Stage II - From L= 15 to L where MP = 0 

MP = "\\frac{dQ}{dL}" = 90L – 6L2 = 0 divide by 6L = 90 – L = 0 ⇒ L = 90

Stage II - from 15 to 90

Stage III - 90 onward 


b) MPL = 30-L

P"\\times"MPL=10 "\\times "(30-L)=300-10L=20

P"\\times " MPL = W ⇒ 300 – 10L =20 ⇒ 280 = 10L ⇒ L = 28workers


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