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.
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 elasticities, “subsidy incidence” also depends only on elasticities. A $3 subsidy on either side of the market gives exactly the same prices – price paid by consumer and price received by supplier – and quantity and thus identical welfare result.
Consider an economy consisting only of Helen, who allocates her time between sewing dresses and baking bread. Each hour she devotes to sewing dresses yields 2 dresses and each hour she devotes to baking bread yields 6 loaves of bread.
a) Graph Helen’s PPF (Production Possibility Frontier) when she works a total of 8 hours per day. On the horizontal axis, put down the number of loaves of bread per day.
Answer: The PPF has intercepts 16 dress on vertical axis and 48 bread on horizontal axis.
b) What is Helen’s opportunity cost for producing bread?
Answer: 1/3 Dress. The key point is that opportunity cost needs to be expressed in terms of the other good.
c) Now suppose that Helen can trade with the rest of the world. The exchange rate is one dress for two loaves of bread. What should Helen specialise in producing if she trades with the rest of the world? Explain.
Answer: The opportunity cost for the rest of the world for bread is ½ dress. Helen has smaller opportunity cost in producing bread and thus has comparative advantage in bread. Helen should specialise in bread.
d) Illustrate the production point and the consumption possibility frontier for Helen with the option of trade and explain if Helen should trade with the rest of the world.
Answer: Given the opportunity costs, it is cheaper for Helen to specialise in B and trade with the rest of the world. The consumption possibility frontier is maximised when Helen completely specialises and produces 48 B. She can then trade with the rest of the world according to the terms of trade. 48 bread can trade for 24 dresses.
Without trade, the PPF is the one plotted in part (a), which was also Helen’s CPF. Now with trade, her PPF...