ECON 351/ FISCAL ECONOMICS I /PROBLEM SET 1
Dr. Osman Zaim

On Pareto Optimality (Efficiency), First Welfare Theorem
1. A society consists of two individuals named A and B the utility functions of which are defined as U_A=(X_A¹)^a.(X_A²) and U_B=(X_B¹)^b.(X_B²) . Here X_m^k denotes the consumption of individual m of good k, where m=1,2 and k=1,2. Total endowments of the two goods are given as w₁ and w₂. (Off course you should realize that this economy is a two-good-two-individuals economy). Now, using this information answer the following questions:
a. Define the contract curve as an implicit function of X_A¹ and  X_A² .
b. What conditions on a and b ensure a linear contract curve?
c. Derive the utility possibilities frontier. (a=b=1).

2. An economy is made up of two people. The utility function of indiviual A is U_A=(X_A¹).(X_A²) and the utility function of individual B is U_B=2(X_B¹)+2(X_B²)  Individual A’s initial bundle consists of 1 unit of good 1 and zero unit of good 2. Individual B’s initial bundle consists of zero unit of good 1 and 1 unit of good 2.
a. Calculate a competitive equilibrium.
b. Find the locus of Pareto optimal allocations.
c. Is the First Welfare Theorem satisfied?

3. Practice the previous question by changing utility function of individual B as U_B=min(X_B¹,X_B²).

Essay Questions:
1. Discuss Nozick's (1974) "Contract Theory of State" (Minimal State or Night-Watchman State) concentrating also on
(a) the role it gives to the government;
(b) its deficiencies when compared with Adam Smith's views on government
(c) its implications on income distribution.

2. Discuss the following in attributing a pottential role for the government
(a) First fundamental theorem of Welfare Economics
(b) Second fundamental theorem of Welfare Economics
(c) Prisoner’s dilemma game
(d) Imperfect competition
(e) Externalities
 

3. Consider economic efficiency.
a. What is meant by ‘economic efficiency’?  Explain it intuitively.  Use a graph if helpful to your explanation.
b. One criteria to judge whether or not an allocation is efficient is the Pareto Efficiency criteria.  What is this criteria?  What are some of its limitations?
c. What is the “Invisible Hand Theorem’ (also known as the First Fundamental Theorem of Welfare Economics)?  Explain it intuitively.  Then, use an Edgeworth diagram to graphically demonstrate why two parties, beginning with an ‘inefficient’ endowment of two goods, will engage in voluntary trade until efficiency is achieved (i.e. end up on the contract curve).
 
 

Hints:
a. Work these questions on your own though they will not be graded so that you can learn the subject matter better.
b. If you find the questions difficult, first go back to your lecture notes and textbook and try to solve them on a firm theoretical basis.
c. Make sure that you have read the week 1 articles specified in the syllabus and understood them.
d. These questions will be covered in the first problem session.
e. If you wish you can submit your solutions, these will not be graded but feedback will certainly be given in the office hours.