EC 3200 Economics of Public Policy Exam Questions

Answer T*W*O 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, *w*e 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.

- Consider two consumers {
*i*=1,2}, each with income M to allocate between a public good*G*

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(G*l) + x1 *= log**(**g! *+*ag*ʻ) + 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) **

- Consider an economy with two consumers of skill levels sį and 82, 82 > $1. Denote the

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

**(10 marks)***(*d) Assuming u(*xh*)*= log(x*h), calculate the marginal rate of substitution for the two

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 **S****aez **(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
**

- Consider an economy with a single consumer whose preferences are given by

*U = log(x*i) + *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 p**roduction technology. Post tax prices of goods 1 and 2 are *91 = p*i + ti and q2 *= P*2 + *t*2 where *t*ị and *t*2 are taxes imposed on good X1 and *X*2 **respe**ctively.

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 s**econd best. (Hint: Compare with

a lump sum ta**x] (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) **

- (a) What are the different types of externalities? Explain using diagrams and examples as

**n****eeded. (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. Howe*v*er, 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 **conseq**uence in the light of the Tragedy of Commons. **(15 marks) **

EC 3200 Economics of Public Policy Exam Questions