1) Suppose the total benefit derived from a given decision, Q, is B(Q) = 29Q - Q

ID: 2506110 • Letter: 1

Question

1) Suppose the total benefit derived from a given decision, Q, is B(Q) = 29Q - Q2 and the corresponding cost is C(Q) = 2 + 2 Q2 .

a. Find the marginal benefit and the marginal cost of Q

b. What is the total benefit when Q = 2? Q=10?

c. What is the marginal benefit when Q=2? Q=10?

d. What level of Q maximizes total benefits?

e. What is the total cost when Q = 2? Q=10?

f. What is the marginal cost when Q=2? Q=10?

g. What level of Q minimizes total cost?

h. What level of Q maximizes net benefits?

a. dB/dQ= 29-2Q dC/dQ= 4Q

b. B= 29*2-2^2 = 54, B= 29*10-10^2=190

c. Q=2: 29-2*2=25; Q=10: 29-2*10=9

d. dB/dQ= 0: q=29/2= 14.5

e. Q=2 : 2+2*2^2= 10; Q=10: 2+2*10^2= 202

f. Q=2: dC/dQ= 4*2= 8; Q=10: =4*10=40

g. dC/dQ=0; so Q=0

h. total benefit B-C= (29Q-Q^2)- (2+2Q^2)= 29Q-3Q^2-2

d(B-Q)/dQ= 29-6Q=0

Q=29/6= 4.83

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