Consider a simple model of a consumer's intertemporal consumption problem. paul lives for two periods, working in the first and retiring in the second. paul earns an income of i in the first period and zero in the second. he must decide how much of his income to consume in the first period and how much to save for consumption in the second period. on any money that paul saves for the second period, paul earns interest at the rate r. so, paul's consumption in period 2 is given by c_2 = (1 + r) (i - c_1) paul's utility function can be written: u (c_1, c_2) = squareroot c_1 + squareroot c_2 (a) if paul has income equal to $100,000 in the first period, and the market interest rate is 10%, how much does paul consume in each period? how much does paul save? (b) if paul must pay income tax at the rate of 25% of income on labor income in the first period, how do your answers change? does the ratio of second period consumption to first period consumption change? why or why not? (c) now assume that paul must pay income tax at the rate of 25% of income on labor income in the first period and also on interest income in the second period. how do your answers to question