Question

In: Economics

A consumer’s income in the current period is y =100, and income in the future period...

A consumer’s income in the current period is y =100, and income in the future period is y’=120. He or she pays lump-sum taxes t = 20 in the current period and t’=10 in the future period. The real interest rate is 0.1, or 10% per period.

a) Determine the consumer’s lifetime wealth.

b) Suppose that current and future consumption are perfect compliments for the consumer and that he or she always wants to have equal consumption in the current and future periods. Draw the consumer’s indifference curves.

c) Determine what the consumer’s optimal current period and future period consumption are, and what optimal saving is, and show this in a diagram with the consumer’s budget constraint and indifference curves. Is the consumer a lender or a borrower?

d) Now suppose that instead of y = 100, the consumer has y =140. Again, determine optimal consumption in the current and future periods and optimal saving, and show this in a diagram/ Is the consumer a lender or a borrower?

e) Explain the differences in your results between (c) and (d).

Solutions

Expert Solution

a)

Current Income = 100

Current Net Income = 100 - taxes

Future Income = 120

Future Net Income = 120 - taxes

Present value of future Net Income = (120-taxes)/1.1

Lifetime wealth = (100-20) + (120-10)/1.1 = 80+110/1.1 = 80+100 = 180

b)

Since current and future consumptions are perfect complements the indifference curves are L shaped with kink at point where c= c'

c)

Current consumption = c

Future consumption = c'

The budget constrant can be written as:

c + c'/(1+r) = 180

As c and c' are perfect complements, so c = c'

c + c/(1+.1) = 180

c + 0.91c = 180

c = 94.24

And c' = 94.24

Savings = y - t - c = 80-94.24 = -14.24. Hence the consumer is a borrower.

With the lifetime wealth of 180, the consumer can have 180 units of current consumption or 180/1.1 = 163.64 units of future consumption. The equilibrium is achived where the budget line touches the IC.

d)

Y = 140

Lifetime wealth = (140-20) + (120-10)/1.1 = 120+110/1.1 = 120+100 = 220

The budget constrant can be written as:

c + c'/(1+r) = 220

As c and c' are perfect complements, so c = c'

c + c/(1+.1) = 220

c + 0.91c = 220

c = 115.18

And c' = 115.18

Savings = y - t - c = 120-115.18 = 4.82. Hence the consumer is a Lender

With the lifetime wealth of 220, the consumer can have 220 units of current consumption or 220/1.1 = 200 units of future consumption. The equilibrium achieved where the budget line touches the IC.

e)

With the increase in current income the consumer is able to save and thus he is lender when his income increases.


Related Solutions

A consumer’s income in the current period is y =100, and income in the future period...
A consumer’s income in the current period is y =100, and income in the future period is y’=120. He or she pays lump-sum taxes t = 20 in the current period and t’=10 in the future period. The real interest rate is 0.1, or 10% per period. a) Determine the consumer’s lifetime wealth. b) Suppose that current and future consumption are perfect compliments for the consumer and that he or she always wants to have equal consumption in the current...
Fact I: A consumer receives income y in the current period, income y’ in the future...
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...
Assume a consumer who has current-period income y=200, future period income y’=150, current taxes t =...
Assume a consumer who has current-period income y=200, future period income y’=150, current taxes t = 40, and future taxes t’= 50, and faces a market interest rate of r=5 percent or .05. The consumer would like to consume such that c’=c*(1+r) if possible. However, this consumer is faced with a credit market imperfection, in that no borrowing is allowed. That is s must be greater or equal to zero.   a. Show the consumer’s lifetime budget constraint and indifference curves...
1. Consumer’s utility function is: U (X,Y) = 10X + Y. Consumer’s income M is 40...
1. Consumer’s utility function is: U (X,Y) = 10X + Y. Consumer’s income M is 40 euros, the price per unit of good X (i.e. Px ) is 5 euros and the price per unit of good Y (i.e. Py) is 1 euro. a) What is the marginal utility of good X (MUx) for the consumer? b) What is the marginal utility of good Y (MUy) for the consumer? How do I calculate these?
Consider a two-period model in which the consumer receives income of y in the current period...
Consider a two-period model in which the consumer receives income of y in the current period and y' in the future period. Rather than imposing lump-sum taxes, the government imposes a proportional tax on consumption. In the current period the tax rate is σ and in the future period the tax rate is σ'. As a result, the government collects σc in goods in the current period and σ'c' in goods in the future period. Since G and G' are...
: Suppose that the representative consumer’s preferences over current consumption (C) and future consumption (C 0...
: Suppose that the representative consumer’s preferences over current consumption (C) and future consumption (C 0 ) are given by the following utility function U(C, C0 ) = CC0β The market real interest rate is denoted by r and β > 0. 1. Write down the consumers’ budget constraint for the current and future period. 2. Using the equations in part (1), obtain the inter-temporal budget constraint. 3. Set up the consumer’s optimization problem using the Lagrangian approach. Next, derive...
An economy has the production function Y=0.4(K+N). In the current period, K=100 and N=100. Graph the...
An economy has the production function Y=0.4(K+N). In the current period, K=100 and N=100. Graph the relationship between output and capital, holding labor constant at its current value. What is the MPK? Graph the relationship between output and labor, holding capital constant at its current value. Find the MPN for an increase of labor from 100 to 110. Compare this result with the MPN for an increase in labor from 200 to 210.
Fact I: A consumer receives income y in the currentperiod, income y’ in the future...
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...
1.     Suppose a consumer has an income of $100. P1=10 and p2=10. a. Draw the consumer’s...
1.     Suppose a consumer has an income of $100. P1=10 and p2=10. a. Draw the consumer’s budget constraint b. On the same drawing, add an indifference curve on which the optimal basket lies. Assume the indifference curve is convex as usual c. On the same drawing, add an indifference curve which has a lower utility level than the optimal basket. Make sure to include the intersections of the curve with the budget constraint, and carefully explain why they cannot be...
Suppose current income increases for consumers, but there is no change in expected future income. Describe...
Suppose current income increases for consumers, but there is no change in expected future income. Describe and illustrate the impact on current consumption, future consumption, and savings. If any of these effects are indeterminate, explain why.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT