Question

A consumer receives income y in the current period, income yœ in the future period, and pays taxes of t and t œ in the current and future periods, respectively. The consumer can lend at the real interest rate r. The consumer is given two options. First, he or she can borrow at the interest rate r but can only borrow an amount x or less, where x < we - y + t. Second, he or she can borrow an unlimited amount at the interest rate r2, where r2 > r. Use a diagram to determine which option the consumer chooses, and explain your results

Answer 1

Answer: Given consumer income ay = Yoe incurrent period in future period pays taxel = t current period = toe in furture period. real interest rate=r x <we-ytt 82>r The option that consumer chooses and why - from the problem the consumers corrent period income isy and pays tax in the arent period. • The consumers future period income is y' and pays taxt'! in future period. • This means that her current perpod endowment 18 Cy-t) and future entow ment is Cy=+') Her real interest lending rate is g.

She is provided with the following optime: O optiml; she can borrow at interest rate of a maximum amount of y, where x is less than we-yt, (i) a< we-ytt. Hefarrent endowment is y-tand linfetime endowment is cue' figure (la) shows the budget line for the consumer. The consumers indifference cene is denoted by I, and Ćdenotes the consumption in the present period while c' depicts consumption in the future period. since her total endowment equatim is: c-x=yt which can be represented as c=y-t+X. it 1. The budget line becomes vertical at point A of

Figure 1(a)

is the maximum amount the consumer Can consume today. It is observed from the figure that a change in the level of a will have no effect on the consumes because the constraint is non binding and she chooses point E figure llais shown as above on the other hand figure 1 (6) the consumer chose a corner Solution and the utility with respect to indifference are I,. . cohen x increased, the consumer's budget constraint is expanded and the consumer now, chooses point El. • In this case, the consumer is more inclined towards Current consumption than future consum ptim. for the debt and lower savings This implies higher future. fails due to In this case, Ricardian Equivalence the changes in lumpsum taxes.

Figure 1 (b)

The consumers in difference are changes to I2. figure 1 (6) is as shown above (2) optim(); . In this case, the consumers would eithers lend or borrow at the same real interest rate and face a maximum amount of borrowing, a The second possPbility is that the interest rate paid on borrowing is more than the interest rate received on lending provided, unlimited borrowing is allowed. like lenders In this case, the consumer behaving would be unaffected by constraints. • Thus the focus should be narrow downed to the Consumers behaving as borrowers. possible cases the constraints a There are two types of impose a maximum amount of borrowing and the constraints

impose a higher rate of interest on borrowing • Both the cafes have been shown as in figure 2 (a) and figure 2(6) The continer will choose best constraint on the basis of preferences between the current and future Consumption, which is determined by the shape of the indifference arres. figure 2 (a) shows that she prefers to pay a higher rate of interest on borrowing. • The kinked budget line (at point A) is also shown. • The consomer is inclined more towards asment Consump- - tion, that is cohy she chooses point El · The higher the indifference Come, the higher will be the utility. • The highest choosen at the point, is by the consumer, Cie)

Figure 2 (a)

Iz with point E". figure 2(a) is as above lo figure 2(b) on the other hand shows that the consumer prefers the constraint of maximum borrowings. . In this case, the preferences are equally inclined towards current and future consumptions, • The consumer might pick point E". This shows that such consumer will chose point e" to any other point on the budget line having a different slopes. · figure -2(b)isas shown below

Figure 2 (b)