The demand curve for product x is given by qxd 300 - 2px

Question

1. The demand curve for product X is given by Q_X^d = 300 - 2P_X.

a. Find the inverse demand curve.

b. How much consumer surplus do consumers receive when P_x = $45?

c. How much consumer surplus do consumers receive when P_x = $30?

d. In general, what happens to the level of consumer surplus as the price of a good falls?

2. You are an assistant to a senator who chairs an ad hoc committee on reforming taxes on telecommunication services. Based on your research, AT&T has spent over $15 million on related paperwork and compliance costs. Moreover, depending on the locale, telecom taxes can amount to as much as 25 percent of a consumer's phone bill. These high tax rates on telecom services have become quite controversial, due to the fact that the deregulation of the telecom industry has led to a highly competitive market. Your best estimates indicate that, based on current tax rates, the monthly market demand for telecommunication services is given by Q^d = 350 - 4P and the market supply (including taxes) is Q^S = 4P - 130 (both in millions), where P is the monthly price of the telecommunication services.

The senator is considering tax reform that would dramatically cut tax rates, leading to a supply function under the new tax policy of Q^S = 4.3P - 130. How much money per unit would a typical consumer save each month as a result of the proposed legislation?

3. Answer the following questions based on the accompanying diagram:

a. How much would the firm's revenue change if it lowered price from $12 to $10? Is demand elastic or inelastic in this range?

b. How much would the firm's revenue change if it lowered price from $4 to $2? Is demand elastic or inelastic in this range?

c. What price maximizes the firm's total revenues? What is the elasticity of demand at this point on the demand curve?

4. The demand curve for a product is given by Q_X^d = 1,200 - 3PX - 0.1PZ where P_z = $300.

a. What is the own price elasticity of demand when P_x = $140? Is demand elastic or inelastic at this price? What would happen to the firm's revenue if it decided to charge a price below $140?

b. What is the own price elasticity of demand when P_x = $240? Is demand elastic or inelastic at this price? What would happen to the firm's revenue if it decided to charge a price above $240?

c. What is the cross-price elasticity of demand between good X and good Z when Px = $140? Are goods X and Z substitutes or complements?

5. Suppose the own price elasticity of demand for good X is -3, its income elasticity is 1, its advertising elasticity is 2, and the cross-price elasticity of demand between it and good Y is -4. Determine how much the consumption of this good will change if:

a. The price of good X decreases by 5 percent.

b. The price of good Y increases by 8 percent.

c. Advertising decreases by 4 percent.

d. Income increases by 4 percent.

6. Suppose the own price elasticity of demand for good X is -3, its income elasticity is 1, its advertising elasticity is 2, and the cross-price elasticity of demand between it and good Y is -4. Determine how much the consumption of this good will change if:

a. The price of good X decreases by 5 percent.

b. The price of good Y increases by 10 percent.

c. Advertising decreases by 3 percent.

d. Income increases by 4 percent.

7. Suppose the cross-price elasticity of demand between goods X and Y is -2. How much would the price of good Y have to change in order to change the consumption of good X by 20 percent?