Assignment:
1. (i). When income and substitution effects work in opposite directions the good must be inferior. True or false, explain.
(ii) A rational agent will never respond to a fall in the pace of a commodity by reducing the quantity demanded of that commodity unless the commodity is inferior. True or false, explain.
2. Economy A is producing 2 goods, x and y, using both capital and labour in the production of each good. The labour force can produce either 300 units of y or 100 units of x or any linear combination of the two. The stock of capital can produce either 200 units of y or 400 units of x. The Economy is initially producing ( and consuming) 50 units of x. There is a 10% increase in the stock of capital without affecting the productivity of any of the factors. Therefore,the competitive price of x would fall from 4y per unit to y/2 per unit of x. True or false explain.
3. Consider a competitive industry with downward-sloping demand and free entry. The industry is composed of identical firms with U-shaped average total cost curves. Initially we are in a long run equilibrium.
The government announces that a substantial fixed annual license fee will be imposed on all firms choosing to remain in the industry. How does each of the following change, (a) industry output; (b) output per firm; (c) the number of firms active in the industry.
Suppose that instead of the license fee, the government Imposes a per unit sales tax. Relative to the original situation with no tax, what is the long run effect on (a) output per fine (b) the number of firms active in the industry.
If the per unit sales tax was adjusted in such a way that aggregate output is the same as under the case of a license fee will the per unit sales tax raise more or less revenue than the license fee? Explain.
4. (a) A consumer has a utility function U(x1, ,x2 ) = [x12 + x21/2]2
Find the Marshallian demand functions for x1; and x2.
(b) In order to aid the poor, the government introduces a scheme whereby the first 1 kg of butter a family buys is subsidized and the remaining amounts are taxed. Consider a family which consumes butter and is made neither better off or worse off as a result of this scheme. The total amount of tax it pays cannot Exceed the subsidy it receives. Analyse whether this daim is true or false.