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Question II Interest Rates Consider a two-period economy consisting of people with identical preferences and identical endowments. There are two consumption goods, one for each period (Ci and C2); the goods have prices P1 and P2, respectively. The endowment of the first period is the same as the endowment for the second period. The preferences are of the form U(C1, C2) = In(C1) + 0.99 * In(C2) The number of people in the economy is irrelevant because they all have the same preferences and endowments. You can use 1, 2, or even a million consumers in this analysis. Select numbers that make your analysis easier. It does not matter what units we use to measure the endowment (pounds, tons, cartons) because everyone has the same endowment. Select numbers that make your analysis easier. 1. Assume the first good has a price of PI-$1. What is the market-clearing price of the other good? 2. What is the interest rate between period one and period two? 3. There is a significant drought in the world and the endowment for period two declines by 10%. Period 1 consumption goods are already harvested, and hence that endowment is unchanged. Use the model to determine the size and direction of the effect on interest rates. Explain your results. Consider a three-period economy consisting of people with identical preferences and identical endowments. There are three consumption goods, one for each period (C1, C2, and C3); the goods have prices P1, P2, and P3, respectively. The endowment is the same in each period. The preferences are of the form U(C1, C2) = In(Ci) + 0.99 * In(C2) + 0.992 * In(C3) 4. Assume the first good has a price of PI=$1. What is the market-clearing price of the other goods P2 and P3? This involves solving a system of equations. 5. What is the interest rate between period two and period three