In the two-period model, suppose a household's income in the first period is $50,000, income in the second period is $60,000, and the real interest rate is 25 percent. Draw a diagram showing the budget constraint. Now, suppose the real interest rate declines to 20 percent. Draw the new budget constraint. For the budget constraints you have drawn, be sure to show the values of the intercepts on each axis. If the household decides that its consumption in period 1 should always be one half of the present value of income, determine whether the household is worse off or better off because of the decline in the real interest rate. Show your work.

What will be an ideal response?


Initial situation: intercept for first-period consumption axis = 50,000 + 60,000/1.25 = 98,000; intercept for second-period consumption axis = 12,500 + 50,000 + 60,000 = 122,500.

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New situation: intercept for first-period consumption axis = 50,000 + 60,000/1.2 = 100,000; intercept for second-period consumption axis = 10,000 + 50,000 + 60,000 = 120,000.

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Budget constraint rotates counterclockwise, from AB to CD.

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In the initial situation, the household consumes 98,000/2 = 49,000. So, the household saves 1,000.

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In the new situation, the household consumes 100,000/2 = 50,000, so the household does not save or borrow. Because the household in the new situation consumes at the no-borrowing, no-lending point, the household is worse off. Why? Because in the initial situation the household could have chosen to be at the no-borrowing, no-lending point but chose not to. So the initial situation must have been a better point for the household.


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