EC 3200 Economics of Public Policy Exam Questions
Answer TWO questions ONLY. All questions carry equal marks (50 marks each). Answer each question in a separate answer booklet.
Approved pocket calculators are allowed.
Read carefully the instructions on the answer book provided and make sure that the particulars required are entered on each answer book. If you answer more questions than are required and do not indicate which answers should be ignored, we will mark the requisite number of answers in the order in which they appear in the answer book(s): answers beyond that number will not be considered.
and a private good x‘. gi represents the contribution to public good by individual i while Go captures the total consumption of the public good by individual i. The public good provides 1 unit of consumption to its purchaser and a units of consumption to the other consumer. Thus, consumer 1 and 2 has utility functions represented by respectively:
Ul = log(Gl) + x1 = log(g! +agʻ) + x1
U? = log(G) + x2 = log(ag+) + x2
(a) Assume a = 1, find the Nash Equilibrium levels of public good contribution and hence,
the total public good consumption when both goods have a price of 1. (10 marks)
(b) Again, assume a = 1, find the efficient level of public good consumption that maximises
the sum of utilities. [Hint : Use symmetry to get the results] (10 marks) (c) Now, assume 0 <a < 1. Provide an interpretation for a. Find the Nash Equilibrium
levels of public good contribution and hence, the total public good consumption when both goods have a price of 1. (10 marks)
Again, assuming 0 <a < 1, find the efficient level of public good contribution that maximises the sum of utilities. For what values of a does private provision coincide with
the socially efficient level? (Hint: Use symmetry to get the results (10 marks) (e) Explain your result when a = 0) and a 0. What happens as a moves towards 1? EC 3200 Economics of Public Policy Exam Questions
When does free riding take place in this context? (10 marks)
allocation to the low skill consumer by (x1, zı) and that to the high skill consumer by (x2, 22).
(a) For the utility function U = u(x) – , write down and explain the incentive
compatibility constraints for the consumers. Show that this requires
22 = 21 + $2[u(x2) – u(x1)]. (5 marks) (b) For the utilitarian social welfare function:
W = u(51) – + (82) –
set up the optimisation problem of the government and express W as a function of X1
and x2 only. (10 marks) (c) Now assume u(xh) = log(In), derive the optimal values of 21 and 22 and hence, 21 and
consumers at the optimal allocation. What can you conclude about the marginal tax
rates for the two consumers? (15 marks) (1) The Mirrlees model predicts a no distortion at the top result. On the other hand
Diamond and Saez (2011) made a recommendation that very high earnings should be subject to rising marginal rates. Comment on this recommendation by Diamond and Saez (2011) in light of the no distortion at the top result of the Mirrlees model. (10 marks) EC 3200 Economics of Public Policy Exam Questions
U = log(xi) + log(x2) + I where xi and x2 are the consumption levels of goods 1 and 2 respectively while I is leisure. Assume that both the goods are produced using labour alone using a constant returns to scale production technology. Post tax prices of goods 1 and 2 are 91 = pi + ti and q2 = P2 + t2 where tị and t2 are taxes imposed on good X1 and X2 respectively.
Using T to denote the consumer’s total endowment of time, explain the budget constraint denoted by:
91X1 + 92X2 + wl = WT
(5 marks) (b) Find the consumer’s demand for the two good x1 and 22. Does this satisfy the
conditions required for the inverse elasticity rule? Assume pre tax prices of both goods
as well as leisure to be 1. (10 marks) (c) Use the inverse elasticity rule to show that both goods should be subject to the same
level of tax. Interpret your answer. (10 marks) Calculate the tax required to obtain a revenue level of R= 1. Using the tax rate that you have calculated, show that commodity taxes are second best. (Hint: Compare with
a lump sum tax] (15 marks) (e) Angus Deaton (1997) studied the demands for commodities in several developing
nations. His analysis of the data from Pakistan is particularly interesting. In 1984-85, the Pakistani government was paying subsidies of 40% on wheat so that consumers paid 40% less than market price for these goods. It also collected 5% tax on oils and fats. Demand for wheat was price inelastic with a price elasticity of -0.64 while demand for oils and fats was very price elastic (-2.33). Does this comply with the Ramsey rule? Explain. (10 marks)
needed. (20 marks) (b) Can government assignment and enforcement of property rights internalise an
externality? Explain. (15 marks) The Grand Banks off the coast of Newfoundland was described as home to an endless supply of cod fish. In the 1960s and 1970s advances in technology allowed huge catches of cod. For nearly 500 years the Grand Banks offered up their amazing harvest. However, in 1992 the fishery was formally closed, throwing thousands of Canadian fishermen out of work; it has not reopened and it seems unlikely that it will. Explain this consequence in the light of the Tragedy of Commons. (15 marks)
EC 3200 Economics of Public Policy Exam Questions