. Your firm’s research department has estimated total benefits to a project to b
ID: 1223401 • Letter: #
Question
. Your firm’s research department has estimated total benefits to a project to be B(Q) = 600Q – 12Q2 and your total costs to be C(Q) =20Q2. a. Take the first derivative of total benefits to find the formula for marginal benefit (MB). b. Take the first derivative of total costs to find the formula for marginal cost (MC). c. What level of Q maximizes net benefits? d. What is marginal benefit at this level of Q? e. What is marginal cost at this level of Q? f. If the firm produces at the point where net benefits are maximized, what are the expected total benefits and totals costs?
Explanation / Answer
(a)
MB = dB(Q) / dQ = 600 - 24Q
(b)
MC = dC(Q) / dQ = 40Q
(c)
Net benefits are maximized when MB = MC
600 - 24Q = 40Q
600 = 64Q
Q = 9.375
(d)
When Q = 9.375, MB = 600 - (24 x 9.375) = 600 - 225 = 375
(e)
When Q = 9.375, MC = 40 x 9.375 = 375
(f)
B(Q) = (600 x 9.375) - (12 x 9.375 x 9.375) = 5,625 - 1,055 = 4,570
C(Q) = 20 x 9.375 x 9.375 = 1,758
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