Please answer all three of the Following questions. Assume a consumer has current-period income y=2, future-period income y'=l SI}, current and future taxes Fill] and t'=SCI. respectively, and faces a market real interest rate ofr=l1i or 5% per period. The consumer would like to consume equal amounts in both periods; that is. he or she would like to set c=c", ifpossible. However, this consumer is faced with a credit market imperfection in that he or she cannot borrow at all: that is, saying sift. ta} Show the consumer's lifetime budget constraint and indifference curves in a diagram. tb} Calculate his or her optimal current-period and future-period consumption and optimal saving, and show this in your diagram. tc} Suppose that everything remains unchanged. except that now t=2 and t"=? I. Calculate the effects on current and iture consumption and optimal saving. and show this in your diagram. td} Now, suppose alternatively that y=l 00. Repeat parts {a} to (ct, and explain any differences. Suppose that there is limited commitment in the credit market but lenders are uncertain about the value of collateral. Each consumer has a quantity of collateral H but from the point of View ofthe lender. there is a probability a that the collateral will be worthy: in the future period and probability I- a that the collateral will be worthless in the future period. Suppose that all consumers are identical. ta} Determine the collateral constraint for the consumer. and show the consumer's lifetime budget constraint in a diagram. tb} How will a decrease in u affect the consumer's consumption and savings in the current period, and consumption in the iture period? Explain your results. A war breaks out that is widely expected to last only one year. Show how the effect ofthis shock on aggregate output depends on the size ofthe intertemporal substitution effect of the real interest rate on current leisure. and carefully explain your results. Draw diagrams for the labour and goods market. and the production function. Provide a detailed economic analysis explaining your results with the aid ofthe diagrams