1. The individual faces a budget constraint in period 1 of Pīc1+81 2 budget constraint of P,C2 = (1+r)s1. Interpret each of these two constraints in =Y and a period words.
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- Consider the intertemporal consumption problem of Mr Cronus between two periods, say this yearand next year. His utility function takes the form U (c1; c2) = pc1 +0:97pc2, where c1 and c2 arehis consumption this and next year respectively. It can be shown (and you do not have to) thatthis utility function satis es diminishing marginal rate of substitution.His yearly income is stable at 100 unit (let say a unit is ten-thousand). He faces di¤erent interestrates between borrowing and saving. Speci cally, the saving interest rate is 0:02, whereas theborrowing interest rate is 0:04.(a) Describe the budget set facing Mr Cronus.(b) Is Mr Cronus a borrower? Explain your answer.(c) Is Mr Cronus a saver? Explain your answer.Consider a two-period consumption saving model and let f1 and f2 denote the first and secondperiod consumption, respectively. Assume that the interest rate at which the consumer may lend or borrowis 10%. Suppose that a consumer’s utility function is x (f1> f2) = f1 + 20√f2= The consumer first periodincome 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-periodsaving? (Make sure to take into account the effect of the decline in the interest rate on the present value ofthe consumer’s income stream.)Explain how does adecrease in the current income y affect the consumer’s consumption-saving decision. In particular,explain: 1) How will current consumption c, future consumption c', and savings s change; 2) Arethere any substitution effect or income effect. Make sure you draw two figures, one for the borrowersand one for the lenders.
- Explain how does adecrease in the current income y affect the consumer’s consumption-saving decision. In particular,explain: 1) How will current consumption c, future consumption c′, and savings s change; 2) Arethere any substitution effect or income effect. Make sure you draw two figures, one for the borrowersand one for the lendersQUESTION 1An individual lives for two periods and decides how much to consume in each period.- In the first period his consumption equals C1 and his income Y1 = 200- In the second period his consumption equals C2 and his income Y2 = 100He can save or borrow money in the first period to finance his consumption in the second period.The interest rate he gets in case he saves or has to pay in case he borrows money equals 7%.Determine the budget constraint of this individual. C2 = −0.935·C1 +314C2 =−1.07·C1 +314C2 =−0.8·C1 +314C2 =−1.08·C1 +314 QUESTION 2The total production of a good y is determined by the production function y = 3L2/3K1/3, where L is labour input and K capital input.The reward (factor prices) for labour and capital are, l = 27 en r = 2, respectively.The producer needs to produce 9000 units of good y.How much units of labour will he hire if he wants to miminize his total costs? 1587,4839,953000515,23 QUESTION 3A good is traded on a perfectly competitive…In Irving Fisher’s two period model, if the consumer is initially a saver and the interestrate and the first period consumption increases, then we can conclude that the incomeeffect:a) Was greater than the substitution effectb) Was less than substitution effectc) Exact offset the substitution effectd) And the substitution effect both increased consumption
- Consider a consumer that lives only for two periods. He works in period 1 (and gets income Y1) and moves up the corporate ladder in period 2 (and gets income Y1 < Y2). This consumer has the usual preferences over time: u(C1) + βu(C2) 1. Assume this consumer cannot borrow. What is the consumption in period 1 and period 2? Display graphically. Show the corresponding utility curve. 2. Assume that now the consumer is allowed to save or borrow. Write down the new budget constraint. What is the consumption in period 1 and period 2? Display graphically. Could the consumer be worse off? Could the consumer be better off? Draw budget constraints such that for one of them consumer prefers to borrow and for the other - prefers to save. 3. Assume once again that a consumer cannot borrow, but can borrow and immediately sell some MacGuffins, and in the next period, the consumer must buy back the MacGuffins to return to the lender. Assume that MacGuffin t r a d e s a t P1 > 0 in the first period…Given the utility function: U = ln c + l + ln c’ + l’ and the budget constraint: w(ℎ−l)+(w′(ℎ−l′))/(1+r)=c+(c′)/(1+r) (see pictures of function and constraint) where c = current consumption, c' = future consumption, l = current leisure, l' = future leisure, and r is the market interest rate.Suppose that the current wage, w = 20 and the future wage w' = 22. a) What is the optimal value of current consumption, c? b) What is the optimal valueof future consumption, c’*?Q1. Consider the following two-period model of consumption and saving: Utility = C1^0.5 + B*C2^0.5 C1 + C2/(1+r) = Y1 + Y2/(1+r) where Y1 = 4, Y2 = 1, r = 0.17 and B = 0.5. Find a numerical solution for period 1 consumption, C1. (State your answer to 2 decimal places.)
- Problem 4 - Costless Magical MacGuffinConsider a consumer that lives only for two periods. He works in period 1 (and gets income Y1) and moves up thecorporate ladder in period 2 (and gets income Y1 < Y2). This consumer has the usual preferences over time: u(C1) +βu(C2)Assume this consumer cannot borrow.1. What is the consumption in period 1 and period 2? Display graphically. Show the corresponding utilitycurve.Assume that now the consumer is allowed to save or borrow.2. Write down the new budget constraint. What is the consumption in period 1 and period 2? Displaygraphically. Could the consumer be worse off? Could the consumer be better off? Draw budget constraintssuch that for one of them consumer prefers to borrow and for the other - prefers to save.Assume once again that a consumer cannot borrow, but can borrow and immediately sell some ‘MacGuffins’, and in the next period, the consumer must buy back the MacGuffins to return to the lender. Assume that MacGuffins trade at P1 >…If you practice consumption smoothing, O you always spend less than you earn. there will be times in your life when it makes sense to borrow. O you make sure your current consumption matches your current income. O you do not save for the future.Assume Marco is initially borrowing and investing 100, with a return on investment of 50% and an interest rate on borrowing at 10%. The return on investment falls to 5%. Which statements are correct? Select one or more: A. Marco’s decision to continue to invest will depend on his preference between consumption today and consumption in the future. B. Marco will wish to invest and borrow, but he will be worse off than when the return to investment was 50%. C. If he continues to invest and borrow, the dashed line representing his new frontier will start at 105 on the y axis and be shallower than the solid red line, so he’ll continue to invest and borrow D. In the remaining questions, assume the central bank now cuts interest rates so that the real interest rate falls to zero. Marco will still not wish to invest and borrow. E. If he just invests his money in the bank instead, his frontier will cross the x axis at 100 and be steeper than the frontier if he invests.…