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Suppose a short-run production function is described as Q = 1L - (1/800)L2 where L is the number of labors used each hour. The firm's cost of hiring (additional) labor is $20 per hour, which includes all labor costs. The finished product is sold at a constant price of $40 per unit of Q.
a. State the firm's MPL:
b. How many labor units (L) should the firm employ per hour:
c. Given your answer in b, what is the output (Q) per hour:
d. Given your answer in c, what is the resulting profit per hour assuming only labor costs?
e. Using the production function Q = 1L - (1/800)L2. How many units of L would be required to produce 150 units (Q=150). Use the quadratic formula to solve for L.
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