8. Suppose the market for widgets can be described by the following equations: D
ID: 1167040 • Letter: 8
Question
8. Suppose the market for widgets can be described by the following equations: Demand: P 10-Q Supply: P Q-4 a. What is the equilibrium price and quantity? b. Suppose the government imposes a tax of $1 per unit to reduce widget consumption and raise government revenues. What will the new equilibrium quantity be? What price will the buyer pay? What price will the seller receive? c. What is the incidence of the tax for the seller and buyer? d. Is your answer to (c) consistent with the respective price elasticities of supply and demand? Explain! (Calculate the elasticities).Explanation / Answer
A.
The equilibrium condition is (Demand = Supply).
Demand = Supply
10 – Q = Q – 4
2Q = 14
Q = 7
Now by putting this value to either the demand function or supply function,
Demand: P = 10 – Q
= 10 – 7
= 3
Answer: The equilibrium price is $3 and quantity is 7 units.
B.
Since the government imposes tax (t) of $1, the new price that suppliers receive would be as below:
P (new) = P – t
= P – 1
The new supply function would be as below:
Supply: P (new) = Q – 4
P – 1 = Q – 4
P = Q – 3
Now by equating demand and supply
Demand = Supply
10 – Q = Q – 3
2Q = 13
Q = 6.5
Now by putting this value to either the demand function or supply function,
Demand: P = 10 – Q
= 10 – 6.5
= 3.5
Answer: The new equilibrium quantity is 6.5 units.
Answer: The buyer will pay $3.5.
Answer: The seller will receive ($3.5 - $1 =) $2.5.
Amount of inefficiency = 0.5 × Difference in equilibrium price × Difference in equilibrium quantity
= 0.5 × ($3.5 - $3) × (7 – 6.5)
= 0.5 × $0.5 × 0.5
= $0.125 (Answer)
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.