1. Consider a market described by the following equations: La = a + BP Qs = Q + μP Where a, b, p and μ are parameters. Note that must be less than zero and the other parameters are positive. Answer the following questions. Solve for the equilibrium price and quantity. a. b. Now suppose a specific tax, T > 0, is imposed on this market that has to be paid to the government by sellers. Show in a clearly labeled supply and demand diagram what happens to the equilibrium effectively price received by sellers, and the price paid by buyers. Be sure to label the price received by sellers and the price paid by buyers in terms of P*(T) and T. Set up the equilibrium condition. Then solve for the price paid by buyers, the price received by sellers, and the after tax equilibrium quantity in terms of the parameters of the model and the tax amount T. C. d. Using calculus and the equation that you found for P* in part c, find an expression for the tax incidence on the buyers and determine its sign. Now, show that the formula you found for tax incidence on buyers can be found using elasticities at the market equilibrium before the tax is imposed. How does the tax incidence on buyers depend on the price elasticity of supply? Verify your result with a supply and demand diagram that varies the elasticity of supply at equilibrium. e.
1. Consider a market described by the following equations: La = a + BP Qs = Q + μP Where a, b, p and μ are parameters. Note that must be less than zero and the other parameters are positive. Answer the following questions. Solve for the equilibrium price and quantity. a. b. Now suppose a specific tax, T > 0, is imposed on this market that has to be paid to the government by sellers. Show in a clearly labeled supply and demand diagram what happens to the equilibrium effectively price received by sellers, and the price paid by buyers. Be sure to label the price received by sellers and the price paid by buyers in terms of P*(T) and T. Set up the equilibrium condition. Then solve for the price paid by buyers, the price received by sellers, and the after tax equilibrium quantity in terms of the parameters of the model and the tax amount T. C. d. Using calculus and the equation that you found for P* in part c, find an expression for the tax incidence on the buyers and determine its sign. Now, show that the formula you found for tax incidence on buyers can be found using elasticities at the market equilibrium before the tax is imposed. How does the tax incidence on buyers depend on the price elasticity of supply? Verify your result with a supply and demand diagram that varies the elasticity of supply at equilibrium. e.
Principles of Macroeconomics (MindTap Course List)
8th Edition
ISBN:9781305971509
Author:N. Gregory Mankiw
Publisher:N. Gregory Mankiw
Chapter6: Supply, Demand, And Government Policies
Section: Chapter Questions
Problem 10PA
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Transcribed Image Text:1. Consider a market described by the following equations:
Q₁ = a + BP
Qa
Qs = φ + MP
S
Where a, b, p and μ are parameters. Note that must be less than zero and the other parameters are
positive. Answer the following questions.
Solve for the equilibrium price and quantity.
a.
b. Now suppose a specific tax, T > 0, is imposed on this market that has to be paid to the
government by sellers. Show in a clearly labeled supply and demand diagram what happens to
the equilibrium effectively price received by sellers, and the price paid by buyers. Be sure to
label the price received by sellers and the price paid by buyers in terms of P*(t) and t.
Set up the equilibrium condition. Then solve for the price paid by buyers, the price received by
sellers, and the after tax equilibrium quantity in terms of the parameters of the model and the
tax amount T.
d.
Using calculus and the equation that you found for P* in part c, find an expression for the tax
incidence on the buyers and determine its sign.
e.
Now, show that the formula you found for tax incidence on buyers can be found using
elasticities at the market equilibrium before the tax is imposed. How does the tax incidence on
buyers depend on the price elasticity of supply? Verify your result with a supply and demand
diagram that varies the elasticity of supply at equilibrium.
C.
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