Question

All-Clean is the only company selling all-in-one washer-dryer machines. The price of a machine is P while Q is the quantity of machines sold per quarter. The following equations describe the market for All Clean Machines: Demand: P = 600 - 5Q ♦ Marginal Revenue: MR = 600 - 10Q Total Cost: TC = 2000 + 60Q + 2.5Q2 ♦ Marginal Cost: MC = 60 + 5Q

1. What is All-Clean's profit maximizing quantity? 36

2. What is All-Clean's profit maximizing price? 420

3. What is All-Clean's profit at its profit maximizing quantity? 7720

4. What is the socially efficient quantity of machines that would be sold if the market was highly competitive (perfectly competitive)? 54

5. What is the socially efficient price that machines would be sold at if the market was highly competitive (perfectly competitive)? 330

6. What is the deadweight loss in the market that results from All-Clean's profit maximizing behavior? 210

7. What is the value of consumer surplus in the market that results from All-Clean's profit maximizing behavior? 90

8. If All-Clean could engage in perfect price discrimination, what level of output would they sell to maximize profit?

9. If All-Clean could engage in perfect price discrimination, what would be the value of consumer surplus that results from its profit maximizing behavior?

10. If All-Clean could engage in perfect price discrimination, what is the deadweight loss that would result from its profit maximizing behavior?

Answer 1

All-Clean is acting as a monopoly. So, at profit maximizing point, MR = MC

1. Demand: P = 600 - 5Q; Marginal Revenue: MR = 600 - 10Q

Total Cost: TC = 2000 + 60Q + 2.5Q2 ; Marginal Cost: MC = 60 + 5Q

The required condition for profit maximisation,

MR = MC

or, 600 - 10Q = 60 + 5Q

or, 15Q = 540

or, Q = 36

Hence, All-Clean's profit maximizing quantity is 36 unit.

2. at Q = 36, P = 600 - 5Q = 600 - 5*36 = 600 - 180 = 420

Hence, All-Clean's profit maximizing price is 420 unit.

3. At this price - quantity combination,

Revenue, R = PQ = 36*420 = 15120

Total Cost, TC = 2000 + 60Q + 2.5Q2 = 2000 + 60*36 + 2.5*(36)2 = 2000 + 2160 + 3240 = 7400

Hence, profit = R - TC = 15120 - 7400 = 7720

Hence, All-Clean's profit at its profit maximizing quantity is 7720 unit.

4. At socially efficient condition, P = MC. This is the price setting rule of prefectly competitive maket.

So, the condition requires,

600 - 5Q = 60 + 5Q

or, 10Q = 540

or, Q = 54

Hence, the socially efficient quantity of machines that would be sold if the market was highly competitive (perfectly competitive) is 54.

5. At Q = 54, P = 600 - 5Q = 600 - 5*54 = 600 - 270 = 330

Hence, the socially efficient price that machines would be sold at if the market was highly competitive (perfectly competitive) is 330 unit.

6. In perfect competition,

Consumer surplus = CSPC = (1/2)*(600 - 330)*54 = (1/2)*270*54 = 7290

Producer surplus = PSPC = (1/2)*(330-60)*54 = 17820 - 2000 - 3240 - 7290 = 7290

social surplus, SSPC = 7290 + 7290 = 14580

In profit maximization condition,

Consumer surplus = CSM = (1/2)*(600 - 420)*36 = (1/2)*180*36 = 3240

Producer surplus = PSM = profit + fixed cost = 7720 + 2000 = 9720

Total surplus, SSM = 3240 + 9720 = 12960

deadweight loss = SSPC - SSM = 14580 - 12960 = 1620

Hence, the deadweight loss in the market that results from All-Clean's profit maximizing behavior is 1620 unit.

7. In profit maximization condition,

Consumer surplus = CSM = (1/2)*(600 - 420)*36 = (1/2)*180*36 = 3240

Hence, the value of consumer surplus in the market that results from All-Clean's profit maximizing behavior is 3240 unit

8. In perfect price discrimination or first degree price discrimination, consumer will be charged the maximum they are willing to pay. Hence, the profit maximization will occur at a point where, P = MC

i.e, 600 - 5Q = 60 + 5Q

or, 10Q = 540

or, Q = 54

So, the quantity produced under perfect price discrimination will be same as in perfect competition.

Hence, if All-Clean could engage in perfect price discrimination, the level of output would they sell to maximize profit is 54 unit.

9. As in perfect price discrimination, each consumer is charged with the maximum price they are willing to pay, the consumer surplus will be zero.

Hence, the value of consumer surplus that results from its profit maximizing behavior under perfect price discrimination is zero.

10. The quantity and price in perfect price discrimination is same as the perfectly competitive market. There will be no consumer surplus as it is captured fully by the price discriminating monopolist. Hence, the producer surplus will be equal to the total surplus and there will be no deadweight loss.

Hence, in perfect price discrimination, the deadweight loss that would result from its profit maximizing behavior is zero.