Question

Suppose the market demand-and-supply curves for the gasoline market are as given below. In each case, quantity refers to millions of litres of gasoline per month; the price is the price per litre (in cents).

Demand: P= 300 - 20QD

Supply: P= 120 + 4QS

Given these equations, the equilibrium price is 150 cents and the equilibrium quantity is 7.5 million litres. Compute the total revenue raised by the gasoline tax. What share of this tax is “paid” by consumers, and what share is “paid” by producers? (Hint: if the consumer price were unchanged from the pre-tax equilibrium, we would say that consumers pay non of the tax)

When the government imposes a tax of 36 cents per litre, Q*new = 6 million litres, the price consumers now pay is 180 cents and the price producers now receive is 144 cents.

The total revenue raised by the gasoline tax is $_____ million

The percentage share of this tax revenue is "paid" by consumers is ?

The percentage share of this tax revenue is "paid" by producers is ?

Answer 1

$P_b=300-20Q_d\\ P_s=120+4Q_s\\ (P_b=price~paid~by~buyer)\\ P_s=price~by~supplier)\\ P_{eq}=150cents\\ Q_{eq}=7.5million~cents.\\ Total~revenue(TR)=\$1.125million\\ If ~a~tax~of~ 36cents~is~imposed\\ P_s=P_b-36cents\\ Given~that\\ P_{bt}=180cents\\ P_{st}=144cents\\ Where~P_{bt}~and~P_{st}~are~new~price~for~consumer~and\\ supplier~respectively.\\ Tax~share~of~buyer=180-150\\ =30cents\\ Tax~paid~by~supplier=150-144\\ =6cents\\ Consumer~share=\frac{30}{36}=\frac{5}{6}\\ Supplier's~share=\frac{6}{36}=\frac{1}{6}\\ Total~revenue~raised~by~the~gasoline\\ tax= (180cents-150cents)×7500000\\ =7500000cents\\ \%tax~share~of~consumer= \frac{5}{6×100}×7500030\\ \%tax~share~of~supplier= \frac{1}{6×100}×7500030\\ =12500cents\\$