Question

The following graph shows three indifference curves and budget constraints for a consumer. The consumer is initially consuming at point A, on the indifference curve Ui and is constrained by the budget constraint BC1 (indicated by the blue line) Bc3 10 Ul BC BC 10 Suppose the government provides this consumer a subsidy on good x, which effectively lowers the price of x. This is represented by a of BC1 out away from the origin. The result is this consumer faces a budget constraint that is similar to which leads to him having a utility level of Suppose, instead, the government provides this consumer an income grant that can be used on either good x or y, leaving the prices of the actual goods constant. This is represented by a that is similar to of BC1 out away from the origin. The result is this consumer faces a budget constraint ,which leads to him having a utility level of This income grant would leave the consumer on a indifference curve than the subsidy on good x

Answer 1

Q 1) Since the government now provides a subsidy on good x which effectively lowers the price of good x, this is represented by rotation of BC₁ out away from the origin. As a result of this the consumer can now spend more on good x since its price has reduced and increase its demand of good x. The result is this the consumer now faces a budget constraint that is similar to BC₂, which leads to him having a utility of U₂.

Q2) In this case since the government provides an income grant which can be used on either of the two goods leaving the prices of actual goods constant, the slope of the budget constraint remains constant but the quantity of both the goods that the consumer can now buy increases. This is represented by a shift of BC₁ out away from the origin. The result is this consumer faces a budget constraint that is similar to BC_3, which leads to him having a utility of U₃. The income grant would leave the consumer on a higher indifference curve than the subsidy on good x.

Q3) E(p_x, p_y, U) = 2$\sqrt{}$p_x $\sqrt{}$p_y U

Since U = 2, E = 2 x $\sqrt{}$1 x $\sqrt{}$4 x 2

E = 2 x 1 x 2 x 2 = 8

Since U = 3 now, E = 2 x $\sqrt{}$1 x $\sqrt{}$4 x 3

E = 2 x 1 x 2 x 3 = 12

In order to achieve utility of 2, the consumer would require an expenditure of $8, while to achieve utility of 3 the consumer would require an expenditure of $12. In other words the consumer would need an extra $4 on purchasing power in order to increase their utility from 2 to 3.