Mid Exam Paper
Econ 8069: Business Economics 2013 Tutorial week 7 reference for answers Question 1
Suppose the weekly inverse demand for a certain good is given by P = 10 - Q, and the weekly inverse supply of the good is given by the equation P = 1 + 0.5Q, where P is the price in dollars and Q is the quantity demanded and supplied per week. Suppose that each unit of consumption of this particular good generates $3 of external benefit to the society.
a) Graph the private demand curve, the social demand curve, and the supply curve in this market. Label them clearly.
Answer: Private demand P = 10 – Q. Social demand: P = 13 – Q. Private S = social S : P = 1 + 0.5Q. Graph not plotted.
b) Find the market equilibrium quantity and price.
Answer: 10 – Q = 1 + 0.5Q or Q =6 and P = 4.
c) Find the socially optimal quantity and price.
Answer: 13 – Q = 1 + 0.5Q or Q = 8 and P = 5.
d) At the socially optimal price and quantity in part (c), calculate the consumer surplus and the producer surplus for the society. Answer: CS = ½*8*8 = 32; PS = ½*4*8 = 16.
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e) At the market equilibrium you identified in part (b), calculate the consumer surplus and the producer surplus for the society.
Answer: Consumer surplus is ½*(3 + 9)*6 = 36. Producer surplus is ½*3*6 = 9.
f) At the market equilibrium in part (b), does the externality create deadweight loss compared to the socially optimal quantity and price? If yes, show the area of the deadweight loss on your diagram and intuitively explain why the DWL has occurred.
Answer: Comparing TS areas in the two equilibria, the DWL area is ½*2*3 = 3. Due to the external benefit, private equilibrium gives rise to DWL since MB > MC in equilibrium and some mutually beneficial trade does not occur.
g) The government now wishes to correct this externality by giving a $3 per unit subsidy. Should this subsidy be given to the consumers or the producers? Explain.
Answer: It does not matter. As the tax incidence only depends on
Suppose the weekly inverse demand for a certain good is given by P = 10 - Q, and the weekly inverse supply of the good is given by the equation P = 1 + 0.5Q, where P is the price in dollars and Q is the quantity demanded and supplied per week. Suppose that each unit of consumption of this particular good generates $3 of external benefit to the society.
a) Graph the private demand curve, the social demand curve, and the supply curve in this market. Label them clearly.
Answer: Private demand P = 10 – Q. Social demand: P = 13 – Q. Private S = social S : P = 1 + 0.5Q. Graph not plotted.
b) Find the market equilibrium quantity and price.
Answer: 10 – Q = 1 + 0.5Q or Q =6 and P = 4.
c) Find the socially optimal quantity and price.
Answer: 13 – Q = 1 + 0.5Q or Q = 8 and P = 5.
d) At the socially optimal price and quantity in part (c), calculate the consumer surplus and the producer surplus for the society. Answer: CS = ½*8*8 = 32; PS = ½*4*8 = 16.
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e) At the market equilibrium you identified in part (b), calculate the consumer surplus and the producer surplus for the society.
Answer: Consumer surplus is ½*(3 + 9)*6 = 36. Producer surplus is ½*3*6 = 9.
f) At the market equilibrium in part (b), does the externality create deadweight loss compared to the socially optimal quantity and price? If yes, show the area of the deadweight loss on your diagram and intuitively explain why the DWL has occurred.
Answer: Comparing TS areas in the two equilibria, the DWL area is ½*2*3 = 3. Due to the external benefit, private equilibrium gives rise to DWL since MB > MC in equilibrium and some mutually beneficial trade does not occur.
g) The government now wishes to correct this externality by giving a $3 per unit subsidy. Should this subsidy be given to the consumers or the producers? Explain.
Answer: It does not matter. As the tax incidence only depends on