Question

Fact I: A consumer receives income y in the current period, income y’ in the future period, and pays taxes of t and t’ in the current and future periods, respectively. The consumer can lend at the real interest rate r. The consumer can borrow at the interest rate r but can only borrow an amount h or less, where h < we - y + t, with "we" denoting lifetime wealth.

Clearly illustrate in a graph what happens to the consumer's current consumption, future consumption and saving when hdecreases.

Answer 1

(a) figure 1.1 shows the circumstance of a purchaser who faces an acquiring requirement. He can't acquire more than a sum h, where

h< we-y+t=we-(y-t)

Where ,

Consumer's lifetime wealth is represented by we,

Current income is represented by y,

Current taxes are represented by t,

Income net of tax is represented by y-t,

The greatest sum he can expend in the current time frame is presently his salary net of expense y-t, in borrowing limit h.

Without the borrowing limit , the spending line is LM. The greatest current utilization would be we, whereby  he consumes his entire wealth in the current period, borrowing the amount is we-(y-t),

With credit constraint of h, the budget line is P .

maximuThe budget line is now kinked, becoming vertical at point P, where consumption is at its maximum e=y-t+h.

Presently consider the impact of an expansion in as borrowing limit h. The impact on the purchaser relies upon his inclinations. For the situation appeared in the main chart underneath, the shopper decides to expend at a direct A toward the left of P, so current utilization is not exactly the most extreme conceivable. For this situation, an expansion in as far as possible has no effect, since the customer Is not borrowing up to the limit in any case. . Figure 1.1

(b) The other conceivable case is that of a purchaser who was acquiring however much as could reasonably be expected at first. This is appeared in the figure 1.2. The purchaser initially picks point P, with the goal that he is devouring precisely y-t+h ,• i.e., the greatest conceivable utilization. He is borrowing the maximum amount ,h. The shopper accomplishes the degree of utility relating to aloofness bend t1.

For this customer, an expansion in borrowing limit x is helpful. With a higher borrowing limit the new budget line is The consumer now chooses to consume at point , on the higher lack of interest bend/. His present utilization has expanded, as he is currently ready to acquire more. Since he gets more, his sparing must decrease, his salary being unaltered. Since saving decreases, future consumption must also decrease.

Figure 1.2