Question

Question 2.

(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

a) In this case, the consumer's behavior is not consistent with the axiom of revealed preference. Here, since we are assuming that the consumer utilizes whole income, hence we calculate the income to be 13 units. We also note that in the first case, (5,3) could have been bought as its cost is 11 units. Hence the consumer clearly prefers (3,5) to
(5,3). But in the second case the individual chooses (5,3) when (3,5) was also available which clearly contradicts the previous choice

b) The consumer's endowment is (10,4) when the prices is (2,1) which can be sold to get 24 units of money. Now since the goods are perfect complements which implies that both the goods will be bought in equal amounts. Hence the bundle chosen eventually is (8,8) which gives 8 units of utility.

further when the prices rises to (3,1) which changes the demanded bundle to (6,6). The utility derived decreases to 6 units.