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Economics 4002

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Economics 4002.02 Problem Set 2

Instructions:

1. Please write down your name on the first page of your submission.

 

2. Please read the questions carefully and make sure you answered all of them.
3. Please use the notations for the variables as they are given in the question.

 

1. Consider the Borrowing-Savings model where the consumer has budget constraints for two periods:

                                                                            c + s = y − t                                (1)

                                                                                    c^′ = y^′ − t^′ + s(1 + r).        (2)

Variables with (^′) represent variables in the second period (for example, c means today’s consumption, while c^′ means tomorrow’s consumption). The consumer is endowed with y − t in the current period and y^′ − t^′ in the next period.

1. 1. Using (1) and (2), derive the consumer’s lifetime budget constraint. Show your work as clearly as possible.
   2. Now, using your answer in (a), draw a figure to illustrate the consumer’s lifetime budget constraint. Label its two endpoints, and also label the horizontal axis with current consumption c. What is the slope of the budget constraint?
   3. On your figure in (b), mark the endowment point (y−t,y^′ −t^′) with E. Assuming that the consumer is a lender, illustrate the consumer’s utility maximisation with an indifference curve and the optimal bundle. What is the level of lending?
   4. State the condition (as a mathematical expression) describing utility maximising behaviour and explain its economic meaning within 3 sentences. (Keyword : willingness to trade, opportunity cost)
   5. Assume that there will be a temporary fall in the tax. Carefully explain the income effect and substitution effect on current consumption and future consumption. If you think that either of the effects does not exist, please state so. Compared to the case where the income increase is permanent, in which case the change in current consumption is larger? Explain why.

2. Consider the Borrowing-Savings model again, the consumer has the same life-time budget constraint as in the previous question but is now a borrower.

1. Draw a figure to illustrate the consumer’s lifetime budget constraint. Label its two endpoints, and also label the horizontal axis with current consumption c. Next, mark the endowment point (y −t,y^′ −t^′) with F. Illustrate the consumer’s utility maximisation with an indifference curve and the optimal bundle. What is the level of borrowing?
2. One day, for some unknown reason, the consumer is not allowed to borrow. How does her budget constraint change? Show this change using your figure in (a). Mark a new utility maximising point on the graph as G and explain how the future consumption changes compared to the case in (a).