Question

Question 1. This question looks at effects of a tax. Suppose that the demand and supply of widgets is summarized by the following equations where p is price.

Qd = 200 – 8p
Qs = 2p

Suppose now that the government imposes a tax of ten dollars per unit which is placed on demanders.

a.   What is the price paid by demanders after the tax is imposed?
b.   What is the loss in consumer surplus in dollars by consumers from the tax?
c.   What is the loss in producer surplus in dollars by producers from the tax?
d.   What is the effect on the tax on the real income of society in dollars?

Answer 1

In order to find the price paid by the demander after imposing tax we have to find the current price and quantity at which the market is in equilibrium therefore we have to equate Qd = Qs.

200-8p = 2p

200 = 10p

200/10 = p

Therefore p = 20

As if Qd = Qs we can substitute p = 20

Qs = 2*20 = 40

1) When tax is imposed by 10 dollars in demand function Qd = 200 - 8(p+t)

= 200 - 8p- 8t

= 200 -8p - 80

Qd = 120 - 8p

Qd = Qs

120 - 8p = 2p

120 = 10p

p= 12

Qd = 120 - 8* 12

Qd = 104

The new price is 12