Re: DSE 2009

Posted by Amit Goyal on Feb 27, 2012; 4:40am
URL: http://discussion-forum.276.s1.nabble.com/DSE-2009-tp7296495p7320753.html

Regarding the micro problem:
In situation (b) the govt. supplies fixed quantity of Y through ration shops free of cost. We assume that in this situation he cannot buy (additional) Y from the free markets. We will show that in none of the three cases he is necessarily better off.
Case 1: Suppose
utility function, u(x, y) = xy
price of X, p(x) = 1
price of Y, p(y) = 1
Income = 10
Lets say govt. supply 2 units of Y free of cost.
Situation (a): In optimum he buys (5, 5) and derives u = 25.
Situation (b): In optimum he buys (10, 2) and derives u = 20.

Case 2: Suppose
utility function, u(x, y) = x + y
price of X, p(x) = 2
price of Y, p(y) = 1
Income = 10
Lets say govt. supply 2 units of Y free of cost.
Situation (a): In optimum he buys (0, 10) and derives u = 10.
Situation (b): In optimum he buys (5, 2) and derives u = 7.

Case 3: Suppose
utility function, u(x, y) = min{x, y}
price of X, p(x) = 1
price of Y, p(y) = 1
Income = 10
Lets say govt. supply 2 units of Y free of cost.
Situation (a): In optimum he buys (5, 5) and derives u = 5.
Situation (b): In optimum he buys (10, 2) and derives u = 2.