Consider a two-period consumption saving model and let f1 and f2 denote the first and second period consumption, respectively. Assume that the interest rate at which the consumer may lend or borrow is 10%. Suppose that a consumer’s utility function is x (f1> f2) = f1 + 20√f2= The consumer first period income is L1 = $100 and the present value of her income stream is $330= (a) What is the optimal consumption stream (consumption bundle) of this consumer? (b) Is this consumer borrower or lender? How much does she borrow or lend? (c) What is the effect of a reduction of the interest rate to 5% on the consumer’s optimal first-period saving? (Make sure to take into account the effect of the decline in the interest rate on the present value of the consumer’s income stream.)

How does savings change with changes in y2? Provide some intuition behind this result.

Q3. Consider a utility function with one consumption good q1 and one type of leisure q2   c) Show mathematically and diagrammatically the decomposition of totaleffect.

2. Suppose Jill derives utility from not only consuming goods, but also from enjoying leisure time. Let her utility function be defined as follows: U=C.25.R.75 where C is a consumption good that can be bought at a price of $1 and R is hours of leisure (relaxation) consumed per day. There are 24 hours in a day and leisure is defined as time spent not working. Jill has a job that pays $w per hour, a trust fund that pays her $M per day, and she can work any number of hours per day, L, she desires. C, consumption good; R, Leisure (relaxation); L, labor M, non-wage income; w, wage rate. a. Derive her labor supply function? b. Assume M = $100, at what wage is her quantity supplied of hours = 0?

1) In the IS equation why wasnt G in the calculations.   2)Suppose that with all exogenous variables, including T and M at their original values, households become less confident about the future and reduce their autonomous level of consumption from 200 to 150. Solve for the new values of e, Y and NX. With the help of graphs, explain very carefully the mechanisms by which a new equilibrium is reached.  3)Suppose that with all exogenous variables at their original values, the autonomous part of money demand increases to 70. Solve for the new values of e, Y and NX. With the help of graphs, explain very carefully the mechanisms by which a new equilibrium is reached.

Suppose that there are T periods to maximize over. Show that the intertemporal budget constraint is Ct+2 Yt+2 Yt+1 (1+r) (1+r)² (1 + r)² Ct + Ct+1 (1 + r) + 2+...+ Ct+T+1 (1+r)² \ T = Yt + + +...+ Yt+T+1 (1+r)

3. Consider a parent who is altruistic towards her child, but also cares about her own consumption. The parent's utility over her own consumption and that of her child is up = log(co) +a log(ci) where c is the child's consumption, and a > 0 is the degree of parental altruism. Suppose that the parent can invest in the child's human capital by spending money (e) on her education; education generates human capital h /() and human capital is paid at rate w. The parent has a total income of (a) Write down an expression for the child's future consumption in terms of the parent's choice of e. (b) Now write down the Lagrangian for the parent's decision problem.

Consider a consumer who can borrow or lend freely at an interest rate of 100% per period of time (think of the period as being, say, 30 years, a bit like with a mortgage). So r = 1.0, or 100%. The consumer's two-period utility function is: U = In(ct) + (1/2)In(Ct+1) The consumer earn Y=100 each period, so Y₁=100 and Yt+1 also equals 100. If this consumer is behaving optimally, trying to maximize her lifetime utility subject to the IBC, what's her consumption in period t?

Q7: An individual lives for only two periods and has preferences given by the follow- ing intertemporal utility function: U = lng + aln(1-h₁) + B[lno₂+ a ln(1 — h₂)] (1) where, c₁, c₂ denotes consumption in period 1 and period 2 respectively h₁, h₂ denote the labour supply in period 1 and 2 respectively. Therefore 1-h is the amount of leisure time in period 1. The term 3 is the discount factor. The problem of the individual at period 1 is to choose consumption in both periods and labour supply in both periods subject to the following budget constraints: +8= why and 0₂= w₂h₂ + (1+r)s where s denote the saving, w denotes the wates and r denotes the real interest rate. (a) Provide an economic interpretation of the two budget constraints written above. (b) Combine the two budget constraints written above and prove the economic interpretation of of life time budget constraint. (c) Set the Lagrangean function and find the first order conditions with respect to C₁ C₂, hi and h₂. (d) Find the…

Consider the problem of an individual that has Y dollars to spend on consuming over two periods. Let c, denote the amount of consumption that the individual would like to purchase in period 1 and c2 denote the amount of consumption that the individual would like to consume in period 2. The individual begins period 1 with Y dollars and can purchase c1 units of the consumption good at a price P and can save any unspent wealth. Use sı to denote the amount of savings the individual chooses to hold at the end of period 1. Any wealth that is saved earns interest at rate r so that the amount of wealth the individual has at his/her disposal to purchase consumption goods in period 2 is (1+r)s1. This principal and interest on savings is used to finance period 2 consumption. Again, for simplicity, we can assume that it costs P2 dollars to buy a unit of the consumption good in period 2. 2 The individual's total happiness is measured by the sum of period utility across time, u(cı) + u(c2). Let u(c)…