Question

In: Economics

4. Suppose that the aggregate market demand for good 1 is D(p) = 100 − 1...

4. Suppose that the aggregate market demand for good 1 is D(p) = 100 − 1 /4 p and the market supply is S(p) = p − 100. Buyers are taxed at $8 per unit.

What is the price paid by sellers after the tax is in place?

How much of the tax is borne by sellers?

Find the deadweight loss

Solutions

Expert Solution

Equating demand and supply in pre-tax equilibrium,

100 - (p/4) = p - 100

5p/4 = 200

p = 160

Q = 160 - 100 = 60

The tax will shift demand curve leftward, and new demand function is

D = 100 - (1/4).(p + 8) = 100 - 0.25p - 2 = 98 - 0.25p

Equating with supply,

98 - 0.25p = p - 100

1.25p = 198

p = 158.4 (price received by sellers)

Price paid by buyers = 158.4 + 8 = 166.4

Q = 158.4 - 100 = 58.4

Tax borne by sellers = 160 - 158.4 = 1.6

Deadweight loss = (1/2) x 8 x (60 - 58.4) = 4 x 1.6 = 6.4

Rahul Sunny answered 2 years ago
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