Question

PLEASE DO NUMBER 5 NOT 4 but 5 needs answers from 4 thank you 4. (30 points) Consider the market for trinkets, where the demand and supply aregiven by the formulas:Demand :Quantity=100−PriceSupply :Quantity=−20+2∙Price (a) (10 points) Draw the demand and supply curves, and find the equilibriumprice and equilibrium quantity. (b) (10 points) Imagine that the government introduces a price cap of $30.Compare the consumer surplus before and after the cap is introduced.Are consumers better off or worse off? (c) (10 points) Imagine that now the price cap is reduced to $20. Comparethe consumer surplus after the new price cap with the consumer surpluswithout any cap. Are consumers better off or worse off? 5. (40 points) In the market for trinkets from problem 4, the government decides to introduce a tax on consumption instead of capping the price. Compute the equilibrium price post tax, the price consumers pay, the equilibrium quantitypost tax, the tax revenue, and the deadweight loss from the following taxes: (a) (10 points) A tax rate of $30. (b) (10 points) A tax rate of $45. (c) (10 points) A tax rate of $60. (d) (10 points) With the results from parts (a) to (c), draw the Laffer curve

Answer 1

Question 5

a) Tax = 30

New demand is Q = 100 - (P + 30) and Supply Q = -20 + 2P

70 - P = -20 + 2P

P = 30

P* that seller receive = 30, price that buyer pays = 30 + 30 = 60, and quantity bought, Q = 100 - 60 = 40 units.

Equilibrium price post tax = 30, the price consumers pay = 60, the equilibrium quantity post tax = 40, the tax revenue = Tax*quantity = 30*40 = 1200, and the deadweight loss = 0.5*tax*(without tax quantity - with tax quantity) = 0.5*30*(60 - 40) = $300

b) Tax = $45

New demand is Q = 100 - (P + 45) and Supply Q = -20 + 2P

55 - P = -20 + 2P

P = 25

P* that seller receive = 25, price that buyer pays = 25 + 45 = 70, and quantity bought, Q = 100 - 70 = 30 units.

Equilibrium price post tax = 25, the price consumers pay = 70, the equilibrium quantity post tax = 30, the tax revenue = Tax*quantity = 45*30 = 1350, and the deadweight loss = 0.5*tax*(without tax quantity - with tax quantity) = 0.5*45*(60 - 30) = $675

c) Tax = $60

New demand is Q = 100 - (P + 60) and Supply Q = -20 + 2P

40 - P = -20 + 2P

P = 20

P* that seller receive = 20, price that buyer pays = 60 + 20 = 80, and quantity bought, Q = 100 - 80 = 20 units.

Equilibrium price post tax = 20, the price consumers pay = 80, the equilibrium quantity post tax = 20, the tax revenue = Tax*quantity = 60*20 = 1200, and the deadweight loss = 0.5*tax*(without tax quantity - with tax quantity) = 0.5*60*(60 - 20) = $1200

We have the data for laffer curve

Tax rate	Tax revenue
0	0
30	1200
45	1350
60	1200