Question

NOTE: Give ALL answers to 2 decimal places and assume all units are in $ 1) A firm has a revenue function of R(Q) = 110Q – 6Q^2 and a cost function of C(Q) = 50 + 20Q + 0.5Q^2.

e) Assume the government imposes an fixed setup cost of $50 on the firm. What will the firm’s profit maximizing quantity be? 1 point

f) Assume the firm will have the following current and future flows of profit: $150 today, $140 in 1 year and $180 in 2 years. With the interest rate at 8%, what is the present value (PV) of these profit flows? 2 points

Answer 1

Answer:

R(Q)=110Q-6Q², C(Q)=50+20Q+0.5Q²

e)

With imposition of fixed setup cost of $50, C(Q)=100+20Q+0.5Q²

Profit function P(Q)=R(Q)-C(Q)=110Q-6Q²-100-20Q-0.5Q²=90Q-6.5Q²-100.

To determine the profit maximizing quantity differentiate profit function with respect to Q and equate it to 0. We get

dP(Q)/dQ=90-13Q=0 or 90=13Q or Q=6.92.

f)

Year	Flow of profit	Present Value @8%
0	$150	$150
1	$140	$140/1.08=$129.68
2	$180	$180/(1.08)2=$154.32
Total		$434