Question

Suppose a small town has a single gasoline station. The station has marginal costs of $2 per gallon, and the gas station owner acts as a monopolist by choosing the quantity and price of gasoline to maximize profits.

The town is fairly isolated, and residents of the town account for all of the gasoline demand in the town. The town has an inverse demand curve of P = 10 – Q, where P is the price of gasoline (in dollars per gallon) and Q is the quantity.

Finally, the external costs of consuming gasoline are $3 per gallon.

1. Why does the gasoline demand curve slope down? In other words, if the station sets one price for a period of time and then increases the price, how will households in the town respond to the price increase?

2. What are the profit-maximizing price and quantity of gasoline?

4. Now redraw your diagram from (3), except that you now show the marginal social cost of consuming gasoline. What are the price and quantity that maximize social welfare?

5. Define deadweight loss as the difference between social welfare in (4) and (2). Indicate deadweight loss in your diagram from (4).

6. Suppose the town wants to tax or subsidize gasoline to maximize social welfare. What tax or subsidy should it choose?

Answer 1

A) The CONSUMER equilibrium at any given price is at where,

Marginal utility =price

As consumption Increases , marginal utility Decreases ( diminishing marginal utility). So CONSUMER keep consume at given price till Marginal utility=price.

After that he will only consume more unit if price will decrease. So that is why Decrease in price leads to increase in demand and increase in price Decrease demand.

B)The profit Maximizing price will be at where,

MR=MC

P=10-Q

MR=10-2Q

MC=2

10-2Q=2

2Q=8

Q*=8/2=4

P*=10-4=6

C)

The welfare Maximizing price will be at where ,

Demand equal = supply( new social marginal cost)

10-Q=5

Q=5

P=5

D) deadweight loss is loss of social surplus/ welfare.

Deadweight loss=1/2*5*3=7.5

E) Tax or subsidy equal to external marginal cost.

So tax/ subsidy=3$ per unit