http://www.gmu.edu/departments/economics/bcaplan

Econ 103

Spring, 2000

**HW#3** *(Please TYPE all answers).*

** **

1. Suppose the supply-and-demand equations for the market for textbooks are:

S: Q= -10 + 50P^{S}

D: Q= 200 - 3P^{D}

a. Solve for the equilibrium price and quantity without taxes.

b. Suppose the government passes a law saying
that book__sellers__ must pay a $3 tax on each textbook. What happens to the sticker price
("price tag") of books? The
market quantity?

c. Suppose the government passes a law saying
that book__buyers__ must pay a $3 sales tax on each textbook. What happens to the sticker price of
books? The market quantity?

d. Show that consumers pay the same total price per book regardless of how the tax is collected. In other words, show that the sticker price in (b) equals the sticker price plus the tax in (c).

e. How much revenue does the government collect from the tax?

f. Using S&D diagrams, shade the
government's total tax revenue. Then
use a different kind of shading to indicate the __deadweight costs__ of the
tax.

2. Suppose the supply-and-demand equations for the market for insulin are:

S: Q= -10 + 5P^{S}

D: Q= 200

a. Solve for the equilibrium price and quantity without taxes.

b. If the government imposes a tax on insulin manufacturers of t/liter. How much does the sticker price of insulin increase?

c. How much revenue does the government raise? Are there any deadweight costs of the tax?

3. Suppose the supply-and-demand equations for the market for automobiles are:

S: Q= -10 + 45P^{S}

D: Q= 2000 - 5P^{D}

a. If the government imposes a tax of $100/car, what fraction of that $100 tax do consumers ultimately pay? What fraction do producers ultimately pay?

b. How what is the smallest tax that would reduce the equilibrium quantity to zero? Show the revenue raised and deadweight costs of this tax on a supply-and-demand diagram.

4. Suppose that:

S: Q= a + bP^{S}

D: Q= c - dP^{D}

Prove that for any per-unit tax, the fraction sellers pay is d/(b+d), while the fraction demanders pay is b/(b+d).

5. Suppose that:

S: Q= 10 + 1,000,000P^{S}

D: Q= 50 - 1,000,000P^{D}

a. What __fraction__ of any tax paid would
suppliers and demanders bear?

b. How much revenue would the government raise in this market from a $.01/unit tax?

c. Intuitively explain your answer.

5. In roughly half a page, analyze the incidence of a national sales tax on Internet commerce. Carefully explain: (a) The main groups involved; (b) The supply and demand elasticities of each group; (c) What this implies about the fraction of the tax each group pays; (d) What this implies about the total revenue the government will collect.

6. In roughly half a page, analyze the incidence of a government ban on ATM fees. Carefully explain: (a) The main groups involved; (b) The supply and demand elasticities of each group; (c) What this implies about the fraction of the tax each group pays; (d) What this implies about the total revenue transferred from banks to consumers.

7. In roughly half a page, discuss the
deadweight costs of the Internet tax **OR** the ATM fee ban. Be careful to distinguish deadweight costs
from transfers.