I need C and D only 8. Suppose the market for widgets can be described by the fo
ID: 1167048 • Letter: I
Question
I need C and D only
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
In pre-tax equilibrium,
10 - Q = Q - 4
2Q = 14
Q = 7
P = 10 - 7 = $3
After the tax, new supply function: P - 1 = Q - 4
P = Q - 3
Equating with demand price,
10 - Q = Q - 3
2Q = 13
Q = 6.5
P = 10 - 6.5 = $3.5 (Price paid by buyers)
Price received by sellers = $3.5 - $1 = $2.5
(c)
Tax incidence of buyer = Price paid by buyers after tax - Pre-tax price = $3.5 - $3 = $0.5
Tax incidence of seller = Unit tax - Tax incidence of buyer = $1 - $0.5 = $0.5
(d) With P = $3 and Q = 7,
From demand function: Q = 10 - P
Elasticity of demand (Ed) = (dQ/dP) x (P/Q) = - 1 x (3/7) = - 0.43
From supply function: Q = 4 + P
Elasticity of supply (Es) = (dQ/dP) x (P/Q) = 1 x (3/7) = 0.43
Since absolute value of Ed = Es, demand and supply have equal elasticity, therefore buyers and sellers share an equal tax burden. The answer to (c) is consistent with elasticitiy of demand and supply.
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