1.(42 points) Suppose a public referendum is being held on whether or not to levy a tax on cigarettes.Currently, the supply of cigarettes is given by Qs = -100 + 20P.You estimate the demand for cigarettes to be Qd = 200 - 5P.

You are asked to evaluate the likely effects of a tax on cigarettes equal to $1 per pack of cigarettes.Specifically, you are to file a report which predicts by how much this will reduce the amount of cigarettes sold.You are also asked to estimate the proportion of the tax that will be paid by the cigarette companies (sellers), and the proportion of the tax that will be paid by the smokers (consumers) of cigarettes.

To do this, you will first need to calculate the current price and quantity of cigarettes sold.

a) (6 points) What is the equilibrium price and quantity of cigarettes?

Next you know from your economics class that you will need to know the price elasticity of demand and the price elasticity of supply of cigarettes. (Note: for parts b-e, please leave your answers in the form of a fraction.)

b) (6 points) What is the price elasticity of demand for cigarettes at the equilibrium price?

c) (6 points) What is the price elasticity of supply of cigarettes at the equilibrium price?

Using your answers to b) and c), you are now able to determine what proportion of the tax will be paid by buyers, and what proportion of the tax will be paid by sellers.

d) (6 points) What proportion of the tax will be paid by sellers?

e)(6 points) What price will buyers pay after the tax is imposed?

f)(6 points) What quantity of cigarettes will be sold after the tax??

Finally, a new proposal suggests that the tax should be levied on the cigarette companies instead of the smokers.

g) (6 points) From what you have learned in this class, how should you respond to this proposal?

2.(40 points) Suppose there are two firms in a market who each simultaneously choose a quantity.Firm 1's quantity is q₁, and firm 2's quantity is q₂.Therefore the market quantity is Q = q₁ + q₂.The market demand curve is given by P = 100 - 4Q.Also, each firm has constant marginal cost equal to 28.There are no fixed costs.

The marginal revenue of the two firms are given by:

MR₁ = 100 - 8q₁ - 4q₂

MR₂ = 100 - 4q₁ - 8q₂.

A) (8 points) How much output will each firm produce in the Cournot equilibrium?

B) (8 points) What will be the market price of the good?

C) (8 points) What is the deadweight loss that results from this duopoly?

D) (8 points) How much profit does each firm make?

E) (8 points) Suppose Firm 2 produced 10 units of output.How much output should Firm 1 produce in order to maximize profit? (Hint: Use Firm 1's Reaction Function)

3.(18 points) Suppose there are 6 firms in an industry.The following table gives the total sales of each firm:

Firm #

Total Sales

1

300

2

150

3

120

4

90

5

60

6

30

Calculate the HHI for this industry:

HHI =