Question

The number of bottles of merlot (wine) demanded per year is 2,200-10P, where P is the price per bottle (in U.S. dollars). The number of bottles of merlot supplied is 100P. (5 points) a. Graph the merlot market. Find the equilibrium price and quantity. (12 points) b. The government wants to discourage wine drinking, so it enacts an "ad valorem" tax (not a specific, fixed amount per unit tax) on merlot; the government will tax the sale by 10%, so that the buyer pays 1.1 times the price received by the seller for a bottle of merlot. What are the new equilibrium prices and quantity in the merlot market? How much money does the government collect from the tax? Amend your graph from part (a) to reflect the ad valorem tax.

Answer 1

(a)

Demand : Q = 2,200 - 10P

Supply: Q = 100P

In equilibrium, demand equals supply.

2,200 - 10P = 100P

110P = 2,200

P = 20

Q = 100 x 20 = 2,000

From demand function,

When Q = 0, P = 2,200/10 = 220 (Vertical intercept) & when P = 0, Q = 2,200 (Horizontal intercept).

From supply function,

When Q = 0, P = 0 (Vertical intercept).

In following graph, D0 & S0 are initial demand & supply curves intersecting at point A with price P0 (= 20) and quantity Q0 (= 2,000).

(b)

After the tax, Demand: Q = 2,200 - (10 x 1.1P) = 2,200 - 11P

Equating with supply,

2,200 - 11P = 100P

111P = 2,200

P = 19.82 (Price received by sellers)

Price paid by buyers = 19.82 x 1.1 = 21.80

Q = 100 x 19.82 = 1,982

Tax revenue = 1,982 x (21.8 - 19.82) = 1,982 x 1.98 = 3,924.36

From new demand function,

When Q = 0, P = 2,200/11 = 200 (Vertical intercept) & when P = 0, Q = 2,200 (Horizontal intercept).

In above graph, D1 & S0 are new demand & initial supply curves intersecting at point B with price paid by buyers P1 (= 21.8), price received by sellers P2 (= 19.82) and quantity Q1 (= 1,982).