Question

consider the following short run production function q=100 l-l^2. where q is the output level and l is the labour input. if the price of output in the market is 50 dollars and labour costs 1200 dollars per hour. how many hours would the firm use to maximize profits. what is the profit maximizing level of output?

Answer 1

q = 100 l - l^2, P = 50 dollars, labour costs Pl = 1200 dollars per hour. To maximize profits firm should produce at TP' = 0, where TP = TR - TC = P*q - Pl*l, so:
(P*q - Pl*l)' = 0
(50*(100 l - l^2) - 1200*l)' = 0,
(3800l - 50l^2)' = 0,
3800 - 100l = 0,
l = 38 hours.
The profit maximizing level of output is:
q = 100*38 - 38^2 = 2356 units.