Let the demand for gasoline be P d = 32-4Q d where P d is price per gallon of ga
ID: 1191518 • Letter: L
Question
Let the demand for gasoline be Pd = 32-4Qd where Pd is price per gallon of gas in dollars and Qd is millions of gallons per year consumed in the US. Let the supply for gasoline be Ps= 2 + 2sQs.
Using the point elasticity formula, compute the elasticity of supply and demand in equilibrium? Based on this alone who will bear the larger burden of an excise tax, consumers or producers?
Assume the government imposes a $3 tax on gasoline in an effort to limit carbon admissions. What is the new equilibrium P and Q ?
What portion of the $3 tax is borne by consumers? Does this agree with your answer to (a)? Explain.
What is the deadweight loss of the tax?
What is the CHANGE in consumer surplus (CS) from before to after the tax?
What are government tax revenues?
Graph the supply and demand curves. Show how the excise tax shits the supply curve. Label the area of CS, PS and Tax revenue, and deadweight loss.
Instead of gasoline, assume the Q and P refer to the quantity of college students in thousands and the price of tuition in thousands of dollars. Use the same supply and demand curves but now analyze the effect of 10 thousand dollar tuition credit per student. What is the new equilibrium P and Q? What is the cost of the program to government and?
Did consumer (student) and producer (college) surplus increase and by how much?
Show graphically the impact of the tuition credit (subsidy) and label the CS, PS and government expenses.
Explanation / Answer
In equilibrium quantity demanded is equal to the Quantity supplied.
4Qd= 32-Pd
Qd= 32-Pd/4
Ps= 2 + 2Qs.
Qs=(Ps- 2 )/2
In equilibrium,
(32-P) /4=( P- 2) /2
P=12
Q=(12-2)/2
Q=5
Point elasticity of demand =(P/Q)(Q/P)
Qd= 32-Pd/4
(Q/P) =-1/4
Ed=-1/4*12/5
Ed =-3/5
Supply Curve
Qs=(Ps- 2) /2
(Q/P) =-1/2
Point elasticity of demand =(P/Q)(Q/P)
=-1/2*12/5
Es=-6/5
b. Buyers will face the larger burden of the tax as the demand is comparitively inelastic than supply
c. When the tax of $3 is increased, price increases by $3. The, new price is now 12+3=15
Q=(15- 2) /2
Q=6.5
d. Buyers will pay $2 and producers will pay $1.
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