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Rick purchases two goods, food and clothing. He has a diminishing marginal rate of substitution of food for clothing. Let x denote the amount of food consumed and y the amount of clothing. Suppose the price of food increases from two on a clearly labelled graph, illustrate the income and substitution effects of the price change on the consumption of food. Do so for each of the following cases:
a) Case 1: Food is a normal good.
b) Case 2: The income elasticity of demand for food is zero.
c) Case 3: Food is an inferior good, but not a Geffen good.
d) Case 4: Food is a Geffen good.
Solution:- a) Given the increase in the price of x, we expect to see the following effects: Because the price of x increased, x became relatively more expensive, and y became relatively less expensive. As a result, Rick substitutes away from x in favor ofy. This is represented in the table by a down arrow for x and an up arrow for y in the substitution effect column. Moreover, the increase in the price of x reduced Ricks purchasing power. Since x and y are both normal goods (x being a normal good is given by the problem, y being a normal good is assumed), the reduction in purchasing power causes Rick to purchase less of both x and y. This is represented in the table by the down arrows in the income effect column. The following diagram gives us a graphical representation of the information presented in the table:- b) In this case, we expect to see the following effects this case, Once again, because the price of x increased, Rick substitutes away from x in favor of y . This is represented in the table by a down arrow for x and an up arrow for y in the substitution effect column. However, the information in the income effect column has changed. Since the income elasticity of demand for x is zero, the reduction in Ricks purchasing power has no effect on x. This is represented by the horizontal line for x in the income effect column. (The down arrow for y reflects the fact that we are continuing to assume that yis a normal…

d.) The following diagram gives us a graphical representation of the information presented in the table: c) In this case, we expect to see the following effects: Once again, because the price of x increased, Rick substitutes away from x in favor of y. Moreover, the reduction in Ricks purchasing power reduces his demand for y (a normal good). What is new is that x is an inferior good; that is, the reduction in Ricks purchasing power causes Rick to purchase more x. This is rep resented by the up arrow for x in the income effect column. The following diagram gives us a graphical representation of the information presented in the table: d) In this case, we expect to see the following effects: The last thing to take note of is that the diagram indicates that x is a Giffen good. The diagram indicates that the income effect dominates the substitution effect; that is, the increase in x going from B to C is large than the decrease in x going from A to B.

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