Question

Rachel spends her income between two goods: good x and good y. Her utility function is given by u(x,y) = min{x,y}. The prices of both goods are P0 = 2 and P0 = 2. Her income

2xy

isM0 =12.

1. (a) Compute Rachel’s optimal bundle and call it (x0, y0).

2. (b) Obtain the utility level associated with the optimal bundle (x0, y0) in (a). Call the utility level u0. (1 mark)

   Now, suppose that prices change but Rachel’s income remains the same. The new pricesarePx1 =2andPy1 =1.

3. (c) Compute Rachel’s new optimal bundle and call it (x1, y1).

4. (d) Obtain the utility level associated with the optimal bundle (x1, y1) in (c). Call the utility

   level u1. (1 mark)

5. (e) Compute the compensating variation, E∗(Px1, Py1, u0) − M0, that Rachel needs to receive in order to achieve the old utility level u0 at the new prices Px1 and Py1.

6. (f) Computetheequivalentvariation,E∗(Px0,Py0,u1)−M0,thatRachelneedstoreceive in order to achieve the new utility level u1 at the old prices Px0 and Py0.

Answer 1