Suppose a market exhibits the following forces: Demand: P = 1500 – 0.5Q Supply:

Question

Suppose a market exhibits the following forces:

Demand: P = 1500 – 0.5Q

Supply: P = 150 + 0.25Q

A tax of $30 per unit is proposed on the market to raise government revenue.

A.       What would be the respective tax burdens paid by suppliers and demanders?

B.      What would be the ratio of government revenue raised to dead weight loss?

C.      Thinking/bonus/extra – if the functions above are fairly short-term representations of the forces in the current year and not representative of long-run possibilities, what happens to your answer in B in periods after the current year and into the future?

Explanation / Answer

First find market equilibrium by equating demand and supply functions

D = S

1500 - 0.5Q = 150 + 0.25Q

1350 = 0.75Q

Q* = 1800

P* = $600

A)

Tax burden is calculated using elasticity values

Ed = (dQ/dP)(P/Q) = (-2)(600/1800) = 0.67

Es = (4)(600/1800) = 1.33

Burden on buyers = Es/(Es+Ed) = 1.33/(1.33+0.67) = 67% of $30 = $20

Burden on sellers = Ed/(Es+Ed) = 0.67/(1.33+0.67) = 33% of $30 = $10

B)

The new P = $620 (paid by buyers) and $590 (received by sellers)

New Q = 1760

Government revenue = tQ = 30(1760) = $52800

Deadweight loss = (1/2)(30)(1800-1760) = 600

Ratio = 52800/600 = 88:1

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

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