Suppose that the government wishes to encourage the manufacture and sale of smal

Question

Suppose that the government wishes to encourage the manufacture and sale of small cars. The current supply and demand of small cars are: Qs = (10/9) + (1/9)P;Qd = 100P, where Q is in millions of cars and P is in hundreds of dollars. Now, suppose that the government is considering two alternative plans for encouraging small car sales. Under Plan A, every car manufacturer will receive a $500 rebate from the government for each car sold. Under plan B, every purchaser of a small car will receive a $500 rebate from the government.

Which of the plan is more eective in encouraging sales? Show by computing the equilibrium quantity under each plan.

Explanation / Answer

Qs = (10/9) + (1/9)P

Qd = 100P

According to plan A, subsidising the producers, the quantity supplied equation becomes (10/9) + (1/9) (P+ 500). The supply curve shifts to the right but there would be no change in consumer demand.

In equilibrium, (10/9) + (1/9) (P+ 500) = 100 - P

=> P + 1/9P = 100+ 10/9 + 500/9

=> 10/9P = 390/9

=> P= 39

Q = 100- 39 = 61

Equilibrium quantity would be 61 units.

According to plan B, subsidising consumers would reduce the price paid by them. The demand curve would shift to the right with unchanged supply.

Qd = 100 - (P- 500)

In equilibrium, 100- P+ 500 = -10/9 +1/9P

=> 600 + 10/9 = 1/9P+ P = 10/9P

=> 5400/9 = 10/9P

=> P = $540

and Q = 100 - (540- 500) = 60

In plan A, P = $39 and Q = 61 and in plan B, P = $540 and Q = 60.

Plan B is more effective in encouraging sales as producers get more price by selling comparatively less quantity in this plan.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.