Question

1. Suppose the market for widgets can be described by the following equations:

Demand: P = 10 – Q Supply: P = Q – 4

where P is the price in dollars per unit and Q is the quantity.

1. What is the equilibrium price and quantity?
2. Suppose the government imposes a tax of $1 per unit to reduce widget consumption and raise government revenues. What will the new equilibrium quantity be? What price will the buyer pay? What price will the seller receive? Calculate the DWL (I am looking for a numerical answer for DWL).

Answer 1

a) Set D=S

10-Q = Q-4

10+4 = Q+Q

14 = 2Q

Q = 14/2 = 7

P = 10-7 = 3

b) When a tax is imposed, the supply curve becomes Q-4+1

Setting D=S

10-Q = Q-4+1

10+4-1 = 2Q

Q = 13/2 = 6.5

P = 10-6.5 = 3.5

So, price paid by buyers = 3.5

Price received by sellers = 3.5-1 = 2.5

New equilibrium quantity = 6.5

Government revenue = 6.5*1 = 6.5

DWL = 0.5*(7-6.5)*1 = 0.25