Question

The local community is considering two options to raise money to finance a new football stadium. The first option is to institute a per unit tax on restaurant meals of $2.00. The market demand and supply functions for restaurant meals are:

Qd=80,000-1,000P

Qs=19,000P-220,000

Round to the nearest whole number.

a) Calculate consumer and producer surplus with the per unit tax.

The second option the community is considering implementing is an income tax. If an income tax is implemented, the new demand for the restaurant meals is:

Q'd=79,000-1000P

b) Calculate the level of consumer and producer surplus in the restaurant market with the income tax.

c) Which of the two options will reduce the sum of consumer and producer surplus the least?

Please clearly box your answers.

Answer 1

In case of tax, the demand function for restaurant meals will be:

Qd=80,000-1,000(P+2)

Qs=19,000P-220,000

The equilibrium will be:

80000-1000(P+2)= 19000P-220000

80000-2000+220000=19000P+1000P

298000=20000P

P = 298000/20000 = $14.9

Therefore, suppliers will receive a price of $14.9

Consumers will pay a price of $14.9+$2 = $16.9

Quantity demanded = 80000-1000(16.9) =63000

Quantity supplied = 19000 (14.9) - 220000 =283100-220000=63100

Consumer surplus = 0.5 * 63.1*63100 = $1990805

Producer Surplus = 0.5 *3.3 *63100 = $104115

Total Surplus = $2094920

When income tax is implemented, then equilibrium will be

79,000-1000P = 19,000P-220,000

299000=20000P

P = 299000/20000 = $14.95

Quantity demanded = 79000-14950=64050

Quantity supplied = 19000*14.95 -220000 = 64050

Consumer Surplus = 0.5*65.05*64050 = $2083226.25

Producer Surplus = 0.5 * 3.35*64050 = $107283.75

Total Surplus = $20940510

Therefore, the second option will reduce the sum of consumer and producer surplus the least.