Question

(a) A consumer has a budget constraint which takes the usual form  m ≥ p_xx + p_yy,   (where  m is income and  p_x, p_y   are the prices of x and y  respectively), and is observed to choose (x, y) = (3, 5) when (p_x, p_y) = (1, 2)   and (x, y) = (5, 3) when (p_x, p_y) = (2, 1). Is the consumer’s behaviour consistent with the (weak) axiom of revealed preference?

(b) Suppose an individual has no income, but is endowed with 10 units of x, 4 units of y, and regards  x, y as perfect one-for-one complements: she has utility function given by  u(x, y) = min{x, y}.   How much of x and y  will the individual consume if the prices of  x and  y are p_x = 2, p_y = 1 respectively? How will these choices of  x, y  change if  p_x rises to 3? Is the individual better or worse off as a consequence of this price increase?

Answer 1

1) No the consumer's behaviour is not consistent with WARP. Let us calculate the consumer's income which is 13 units( price*quantity).In the first case, (5,3) is available when the prices is (1,2), but the consumer chose (3,5). Hence (3,5) is revealed prefered to (5,3). But in the second case (3,5) was also available as its cost is 11units but the consumer chooses (5,3) which is a violation of WARP.

2) The consumer is endowed with the bundle (10,4) and the prices presently are (2,1) with a utility of 4 units. If the consumer chooses to sell them, he has an income of 24 units. Since, the goods are complements, the individual would like equal amount of each good. Hence (8,8) is the bundle which will be chosen with a utility of 8units.

Now, if the prices rises the demanded bundle is (6,6). He is worse off with this price rise compared to 8 units achieved earlier, he accrues 6 units now.