Question

1.	Suppose Gerte Guzzler has a daily income of $80. Gerte allocates her income between gasoline, which she uses on her daily commute to work, and clothing, which she wears to work. The price of gasoline is $5 per unit (1 unit = 5 gallons) and the price of clothing is $2 per unit.
a.	How is Gerte affected by a government plan to ration gasoline to 5 units per day? Explain. Use a graph of the consumer choice model to illustrate your answer. [NOTE: Ration controls are to the right of the graph.]
b.	Suppose instead that the government imposed a per-unit tax on the consumption of gasoline (this tax to be paid by buyers). How large would the tax have to be to leave Gerte indifferent between the rationing plan and the tax plan? Explain. Use a graph of the consumer choice model to illustrate your answer.
c.	Will both government plans achieve the same end? Explain.
d.	Is one form of the plan more "fair" than the other? Explain.[HINT: Do you think everyone has the same relative preferences as Gerte?}

Answer 1

Figure (i) is for question (a) and figure (ii) is for question (a) and (b) .

a. Rationing means to allow a person to have a fixed quantity of goods. Here, gasoline is being rationed at 5units per day. The daily income is $80 per day, and the price of gasoline is $5 per unit and that of clothes is $2 per unit.

The budget constraint here will be,

M = G*Pg + C*Pc ( M = Daily income of the person, Pg = price of gasoline, Pc = Price of clothes)

Therefore, by putting the values,

80 = G*5 + C*2

The graph is attached. The budget set of the consumer is the shaded region.

b. When per unit tax is imposed on the consumption of gasoline so that Garte remains indifferent between the rationing plan and the tax plan.

Here, the budget constraint will be,

M = G*(Pg+t) + C*Pc ( the definitions of M,Pg,Cg,G and C remains the same as above, only t=tax)

80 = G *(5+t) + 2C

The graph is attached.

As we do not have any utility function given here, so we cannot find the utility values. By drawing the indifference curve on the graph, we are assuming that 5 units of gasoline is lesser than (80/5+t) units of gasoline. Hence, in this case the interceptions of the two graphs one with the rationing scenario and the other with the tax imposed will be different. If the indifference curve lies on the edge of the curve as shown in the figure then only the two curves will yield the same amount of utility.

c. Both the government plans will achieve the same end if the indifference curve remains the same. So the indifference curve will have to lie on the edge of the budget line of the rationed budget line and again of the tax imposed budget line, as shown in picture (ii).

d. Is one plan fairer than the other depends on the prefr3nxes of the consumer, as the indifference curve changes as per the taste and preference of the consumers.