Question: 1. A consumer lives for two periods (the present and the future). His income in period 1 is 100. His income in period 2 is 200. Prices of the single consumption good are $1 per unit in both periods. The interest rate at which he can lend or borrow is 20% per period. Consumption in the present and the future periods is C1 and C2. The utility function is U(C1,C2)=C1*C2.

a. Solve the optimization problem of the consumer. (Non-round number of units is ok, if that's the solution)

b. Is the consumer a borrower or a lender? Is the result intuitive to you? (please calculate savings explicitly as part of the answer)

c. If the consumer wins the lottery today, and that increases his future, 2nd period income by 300, will he change his borrowing decision? Is the result intuitive to you?

2. Analyze the effect of an interest rate decrease on a consumer who is currently a lender. Specifically, answer the following questions. A graph would be useful in your analysis.

a. What happens to consumption today and in the future?

b. Is the consumer better or worse off?

c. What happens to savings?

d. Will the consumer remain a lender?

3. In a model with uncertainty, there are two "states of the world". In state one, the consumer has a yearly income of $100,000. In state two, the consumer gets hurt in an accident and cannot work, so he has no income. The probability of an accident is 5%.

a. How much will the consumer agree to pay for insurance that gives him $100,000 compensation in case he has an accident if he is risk neutral?

b. Now suppose the consumer is risk averse. He is offered an insurance that will pay him $100,000 in case of an accident. The insurance costs $2500. Will he buy the insurance? Why or why not?

4. Explain in a few sentences. Think and answer using economic terms.

a. Why women are more likely to stay at home and take care of children than men are? Think and answer as an economist.

b. What you expect would happen to (a) if women's salary were to increase so that women make 10% more than men, for the same job.

c. Whether providing a subsidy for day care usage (returning 30% of the day care cost as tax benefits) is likely to affect (a), and for whom (compare different ‘types' of women based on earning potential, skills, number of children, etc.)

5. You are the manager of a small business. Every month, you bring in $22,000 in revenues. You work in your business. You could have worked somewhere else for a salary of $6,000 per month. Your monthly wage expenses payable to other workers are $12,000, and your monthly rent for the business office is $5,000. However, you believe that the owner will allow you to be released from your rent for a compensation of $1,000 per month remaining on the contract. Your monthly expenses for materials needed for the business are $2000. Your expenses for the business license are $2,000 per month. They were already paid for the whole year and cannot be recovered. It is now March.

a. Calculate monthly expenses, revenues and profits using the accounting cost method (assuming the business keeps operating)

b. Repeat (a) using the economic cost method (assuming the business keeps operating)

c. Should you continue operating the business until the end of the year? You may assume no change is going to affect the income and expense streams - i.e. there is no uncertainty.

d. Should you continue operating the business next year? You may assume no change is going to affect the income and expense streams - i.e. there is no uncertainty.