Question 1 (Where does Inequality come from?) Assume that the utility of a consumer over two periods is given by U = u(c) + pu(c') where c is consumption in the current period and ' is consumption in the future period. Consumers pay taxes to the government in both periods. Credit markets are perfect, i.e. interest rates for borrowers and lenders are the same, and everyone always repay its debts. The real interest rate is r. The consumers can be of two types. The rich consumers have an initial financial wealth equal to a. Poor consumers have no initial financial wealth. Each consumer, no matter if rich or poor, will receive an income in the current period and in the second period. For simplicity we will assume that income in the first and second period are identical and equal to y. Taxes paid to the government are also identical in each period and equal to t: a. Derive the intertemporal budget constraint of poor and rich consumers. [10 points] b. Assume g = 1 and u(c) = In (c), where In is the natural logarithm. Calculate the optimal and ' for poor and rich consumers. [10 points] c. As a measure of inequality, we can calculate the ratio of current consumption of rich consumer versus poor consumers, ER How does this depend on the initial P financial wealth of the rich consumers a? How does it depend on taxes and interest rates? Explain. [5 points] Many economists think that a big part of inequality can be explained by difference in educational levels. Rich consumers can finance and reach higher levels of education and therefore are able to get higher-paying jobs later in life. To understand the implications of this, we will assume that for rich consumers, the current period private disposable income is y t, but in the future period it will be (1 + e)y t where you can interpret e as the return to education. Poor consumers are not able to access higher education, and therefore their private disposable income will be equal to y t in both periods. d. Derive the intertemporal budget constraint of poor and rich consumers. [10 points] Assume B = 1 and u(c) = In (c), where In is the natural logarithm. Calculate the optimal and ' for poor and rich consumers. [10 points] We can calculate the ratio of current consumption of rich consumers versus poor consumers, ZR How does this depend on the initial financial wealth of the rich P consumers a? How does this depend on the return to education e? Explain. [5 points] In this economy, would the Ricardian equivalence hold or not? Explain. [10 points]