Answer to Question #307367 in Microeconomics for jane

Question

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 in thousands of units. Then: a. What is the equilibrium price and quantity? [2] b. 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 amount per unit will the seller receive? [5] c. Suppose the government has a change of heart about the importance of widgets to the happiness of the American public. The tax is removed and a subsidy of $1 per unit granted to widget producers. What will the equilibrium quantity be? What price will the buyer pay? What amount per unit (including the subsidy) will the seller receive? What will be the total cost to the government? 

Answer 1

a) At equilibrium, Q's= Qd

Q-4= 10-Q

Q= 7

P= 7-4= 3

b) When tax is imposed

Supply = Q-4+1

Q-3= 10-Q

Q= 6.5

P= 10-6.5= 3.5

Therefore price paid by buyers= 3.5

Price received by sellers= 3.5-1= 2.5

c) When subsidy is given,

Supply= Q-4-1

Q-5= 10-Q

Q= 7.5

P= 7.5-5= 2.5

Price paid by buyers = 2.5

Price received by sellers= 7.5-4= 3.5

Cost to the government= 0.5\times (7.5-7)\times 1= 0.25×(7.5−7)×1=0.25