Question

7) A for-profit firm is bidding on a contract that would make it the sole provider of trash and recycling pick-up services in a city. The city-wide demand for trash and recycling pick-up is given by Qp = 50,000 - 200P where is measured in tons of material picked up and P is the price per ton. That demand curve implies that the inverse demand (i.e., rewriting the demand equation with as a function of P) for trash and recycling pick-up is P = 250 -0.0050. If the firm wins the contract, it will be able to choose price as a monopolist and its marginal revenue curve would be given by Page 1 of 3 MR = 250 -0.010. The firm's marginal cost is constant at $100 per ton, MC = 100, which implies that its total cost is directly proportional to Q. TC = 1000 a. What are the profit-maximizing price and quantity for the firm if it wins the contract? b. In a standard diagram with on the horizontal axis and P on the vertical axis, show your answer to part a. Be sure to show how both price and quantity are determined, and clearly label all relevant curves. Also, show the equilibrium price and quantity of this market were competitive. c. At the monopoly equilibrium from part a, calculate consumer surplus, producer surplus, and deadweight loss. Also, what would consumer surplus be under competition? d. What is the maximum amount the firm would be willing to bid for the contract? Assume that it will not be able to operate in the city unless it wins the bid and will therefore have no profit. c. A consumer advocacy group argues that granting this firm monopoly power hurts city residents/consumers. In response, a city commissioner announces that the firm's contract bid will go back to the residents consumers in the form of lower taxes. In that case, the commissioner argues that consumers will not, in net, be hurt by the granting of monopoly power. Explain why the commissioner is wrong. (Hint: Your answers to parts and should factor into your explanation)

Answer 1

a) Price P = 250-0.005Q

Marginal Revenue MR=250-0.01Q

Marginal Cost MC=100

Total Cost TC = 100Q

Q is the total quantity in tonnes

For a monopolist, Profit Maximization happens when

Marginal Revenue = Marginal Cost

MR = MC

250-0.01Q = 100

0.01Q = 250-100

Q= 150/0.01

Q = 15,000

At Q = 15,000

P=250-0.005*15,000

P = 250-75

P = 175

So the profit maximizing Quantity is 15,000 tonnes and the price is $175 per tonne

b)

Profit Maximizing Chart 250 225 200 200 175 (15000,175) 175. ----- ISO--- 150 100 125 100- 100 100 100 100 100 Price 50 (30000,100) 5000 10000 15000 20000 25000 3 0990 35000 -100 Quantity —MC - MR — Demand Curve (Price)

For a monopolistic Firm, MR = MC for profit maximization. So the point at which the MR and MC Intersects, that is the profit maximizing quantity of 15,000 tonnes. If we extend that vertical line upwards to meet the demand curve, then it meets it at the point (15000,175). This $175 per tonne is the profit maximizing price for the monopoly.

If it is a perfect competition, then Price P = MR = MC

Price P is also given by the demand curve. So the point of intersection of the demand curve and the Marginal Cost curve is the profit maximizing price for a competition. The price is also given by the same point. So the profit maximization quantity is 30,000 tonnes and the price is $100 per tonne

c) From the above diagram,

Consumer Surplus is the area of the blue coloured triangle = 0.5 * (15000-0)*(250-175)

Consumer Surplus = 0.5*15000*75 = $562,500

Producer Surplus is the green coloured rectancle = (15000-0)*(175-100)

Producer Surplus = 15000*75 = $1,125,000

Deadweight Loss is the area of the orange triangle = 0.5*(30000-15000)*(175-100)

Deadweight Loss = 0.5*15000*75 = $562,500

d) Let the maximum price the firm will be willing to bid for the contract be T

So Total cost of the firm at profit maximizing price and quantity = T + 100Q

So Total Cost = T + 100*15,000 = T + 1,500,000

Total Revenue = P*Q = 175*15,000 = $2,625,000

Total revenue should be higher than total cost for the firm to bid for the project.

=> T+1,500,000<2,625,000

=> T < 2,625,000-1,500,000

=> T < 1,125,000

So the maximum price the firm will be willing to bid for the contract will be $1,125,000