l. 2. Suppose Joe earns $1,000 in year 1 and $0 in year 2. Any amount he saves will earn interest at a rate of 10%. Draw Joe's budget line. Assuming convex (normal looking) indifference curves, show that an increase in the interest rate can cause Joe's savings to either increase or decrease. Explain in terms of income and substitution effect. A consumer lives two periods, and derives utility from consumption in the present (period 0) and the future (period 1) according to the following utility function: 0(c..c.)=1n(c.)+m(c.) a. Find the slope of the consumer's indifference curve along the 45 degree line, i.e., when C0 = C1. Based on your answer, what is the interpretation of the parameter rho? [Hintz the derivative of ln(x) is 1. Therefore, marginal utility with respect to period 0 x consumption is M U0 2 CL, and marginal utility with respect to period 1 consumption 0 l 1 1s MUl ] 1+ p C1 b. Assume that the consumer receives income Yo in period 0, and Y1 in period 1, and that he can borrow and lend any amount at interest rate r. Solve the consumer's utility maximization problem, and derive the consumer's savings S (S = Y0 Co) as a function of the parameters Y0, Y1, r and p. 0. Assume that Y0 = Y1. Show that savings is positive if and only if r > p. Assume that Y0 = Y1. In a graph with the interest rate r on the vertical axis and savings on the horizontal axis, draw the savings function as a function of r. Is there any range of r for which the income effect dominates the substitution effect