Question

Exercise 2. A monopolist faces the following demand curve: Q 10,000 100P Where Q is the weekly production and P is the price, measured in S/unit. The firm's cost function is given by C 50Q 30,000. Assuming the firm maximizes profits a. Find the equation describing the marginal revenue curve b. What is the level of production, price, and total profit per week? c. If the government decides to levy a tax of 10 $/unit on this product, what will be the new level of production, price and profit?

Answer 1

Q=10,000 – 100 p (a) loop = 10,000 - 0 p = 10,000 -Q loo P = 100 - Q TR= p.2 TR = 100 Q - RO MR=dTR da = 100(1) -20 100 MR = 100 - a Monopoly TC = SO Q +30,000 MC = dTC da = SO(1) to

MC = so profit maximising MR — ис condition ba y le 100-S ở e Q Q Substituting = soxso = 2500 units. a into Price equation P = loo-2500 100 = 100 - 25 P =$75 TR=P.Q = 75+ 25oo = 187, SOO TC = so (2500) + 30,000 = 12S000 +30,000

TC = 155.000 Profit = TR-TC = 187,500 - 155000 = $32,000 per week. (C) of gout levy a tax = 10 New New demand equation Q = 10,000 -100 (PHO) Q = 10,000 -100p-1000 Q =9,000 -10op loop = 9,000 - p = 9000 - Q 100 p=90 - Q TR = P Q . T12=902. MR = 2TR da = 90(1) - 20 100

vew MR = 9 ora so Condition New New profit-maxiniging MR = mc 90-Q S . So 90 -so = Q + _ 40 = Q 5. Q = yoxso a = 2000 2 = 2000 units, Firm ABC Makes substituting a a loss of into Price $35,766.62 equation

P = 90 - 2000 yo = 90 -so = $40 TR= p.2 = yox2000 = 80,000 TC =50 (2000) +3000 0 =100,000 130 000 = 130,000 Loss = TC-TR = 130,000 -80,000 = $seceo = $ 59,000 Hz