A consumer's income in the current period is = 50 and in the future period is = 200. There are no taxes in this economy hence = = 0. The consumer prefers to have perfectly smooth consumption so consumer's optimal consumption rule is given by: = . The real rate of interest in this economy is = 0.1.

(a) Draw the consumer's life-time budget constraint and identify endowment point. Please indentify the horizontal and vertical intercepts of budget constraint in the diagram. (2 marks)

(b) Draw the consumer's indifference curves and show the equilibrium levels of c and c on the graph. Compute the numerical values for equilibrium c and c. (4 marks)

(c) Now suppose that the lending institutions impose a limit on credit. Specifically, they set a maximum limit x on borrowing in the current period, where = . Discuss how this change will affect the consumer above. Show the new constrained equilibrium, i.e., new c and c in the same graph that you have drawn for part (b). Also compute the numerical values for equilibrium c and c. (2 marks)

(d) Would the consumer in question be affected if the credit limit were set at = 2? (2 marks)