Q1. (a) Consider the following two distributions of income:

A : (2; 8; 14; 20; 26);

B : (1; 5; 6; 10; 13).

Which would you consider to exhibits greater inequality and why?

(b) (Seade)

The figure shows the Lorenz curves for two distributions of income. The coordinates of the points are B (40%, 10%) and C (90%, 60%). Calculate the Gini coefficients for the two distributions.

(c) How would the Atkinson Index rank the distributions depicted above? You must state and explain the assumptions that you make in arriving at your answer.

Q2. A simple economy has 2 consumers, denoted i, i = 1, 2, and a benevolent government. A single consumer good is made with the sole productive factor, labour. The consumers have the same utility function, U(x_i, l) = x_i^1/2 - l_i, i = 1, 2, where x_i is consumer i's consumption of the consumed good and l_i is its labour supply. The consumers have different productive capacities, their skill levels s_i, i = 1, 2, with s₂ > s₁. The government cannot identify a consumer's skill level. However, it can observe consumer earnings. It decides to impose a nonlinear income tax-transfer system to maximise utilitarian social welfare, levying taxes purely for redistributive purposes.

(a) Calculate the optimal tax-transfer system.

(b) Suppose s₂ = 2 and s₁ = 1. What will be the levels of consumption, gross income and taxes or transfers for the consumers?

Q3. "The problem of externalities is just a problem of missing markets. Create the markets and, hey presto, problem solved!" Discuss in no more than 800 words.

Need Question 2 answering.