In the two-period model of consumption, suppose that the first period income is $5,000 and the...

In the two-period model of consumption, suppose that the first period income is $5,000 and the second period income is $5,500 for both Jill and Jack. The interest rate is 10 percent. Jack’s lifetime utility function is ?1 + ?2 while Jill’s lifetime utility function is ?1 + 0.8?2.

1)Draw a graph that represents the common budget constraint that Jill and Jack face.

2)Draw indifference curves of Jill and Jack in separate graphs and compare the slopes of the indifference curves with the slope of the budget constraint curve.

3)Determine the optimal consumption in period 1 and 2, for both Jill and Jack.

4)If there is a borrowing constraint, whose consumption is affected by that?

Solutions

Expert Solution

-----

Rahul Sunny answered 1 year ago

Next > < Previous

Related Solutions

Consider the two-period Neoclassical consumption model seen in class. Suppose that income is measured in dollars....

Consider the two-period Neoclassical consumption model seen in class. Suppose that income is measured in dollars. Let the utility function take the logarithmic form U(C)=ln C, and the representative consumer maximize her lifetime utility subject to her budget constraint. Suppose that income in period 1 is $50,000, income in period 2 is $30,000, ?=1 and ?=5%. Do you think that the consumption profile of the agent in this numerical example is going to be smoother than her income? If so,...

Consider the following two-period Fisher model of consumption. Jamil earns $600 in the first period and...

Consider the following two-period Fisher model of consumption. Jamil earns $600 in the first period and $0 in the second period. The interest rate is 10 percent. His lifetime utility function is log(?1 ) + 0.5log(?2). a) Find the optimal values of ?1 and ?2. Answer: ?? = ???, ?? = ??? b) Suppose that the lifetime utility function changes to log(?1 ) + log(?2). Calculate the new optimal values of ?1 and ?2. How is the optimal value of...

Consider a two-period consumption model where an individual has income It > 0 in period t...

Consider a two-period consumption model where an individual has income It > 0 in period t and the (net) interest rate is r > 0. However, suppose the price levels are not assumed to be 1. Instead, let p2 ≥ p1 > 0. (a) Derive the lifetime budget constraint. (b) What is the slope of the lifetime budget line? Letting 1 + π = p2/p1 bethe gross inflation rate, given an interpretation of the magnitude of them budget line. (c)...

Aji and Mustapha both obey the two-period model of consumption. Aji earns $100 in the first...

Aji and Mustapha both obey the two-period model of consumption. Aji earns $100 in the first period and $100 in the second period. Mustapha earns nothing in the first period and $210 in the second period. Both of them can borrow or lend at the interest rate r. You observe both Aji & Mustapha consuming $100 in the first period and $100 in the second period. What is the interest rate r? Suppose the interest rate increases. In a clearly...

3) Suppose the real interest rate falls in the two-period model (where income and taxes are...

3) Suppose the real interest rate falls in the two-period model (where income and taxes are exogenous). Consider the income and substitution effects and explain in words and through diagrams how this change affects current consumption, future consumption, and savings of a consumer who is a a) lender b) borrower c) Which type of consumer (lender or borrower) becomes better off after the interest rate change? Explain in words.

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...

A more realistic depiction of the two-period consumption model would have a different interest rate for...

A more realistic depiction of the two-period consumption model would have a different interest rate for savers and borrowers. Think about it. The rate you pay for a student loan or a home mortgage (when you are a borrower) is much higher than the rate you earn on a savings account at a bank (when you are a saver/lender). 1 Let r S be the interest rate for a saver and r B be the interest rate for borrower, such...

Consider a general model of intertemporal consumption. Paul lives for two periods, working in the first...

Consider a general model of intertemporal consumption. Paul lives for two periods, working in the first and retiring in the second. Paul’s income is 1000 in the first period and is 0 in the second period. He must decide how much to consume in the first period and how much to save for consumption in the second period. Any money that Paul saves in the first period will earn a 5% interest. For the questions below, you only need to...

Consider the life-cycle model. The agent has income w only in the first period. The interest...

Consider the life-cycle model. The agent has income w only in the first period. The interest rate is r>0 and the utility function of the individual is quasi-linear U(C1,C2)=f(C1)+C2 where f is a function with f'>0 and f''<0. If we establish a tax on capital income, what is it going to happen with savings? Explain your answer

Consider an economy with a real income of $7,000, consumption spending of $5,000, and net tax...

Consider an economy with a real income of $7,000, consumption spending of $5,000, and net tax revenue of $1,000. a. Calculate domestic private saving b. Suppose government spending is $1,000. Calculate public saving. c. Continuing from part b, what is national saving? d. Continuing from part c, suppose net foreign investment is -$2,000. What is private domestic investment spending?

Subjects