18. Chris maximizes discounted utility U(co, c1, c2) co + ốc1 + 8?c2 for 8 0.8. %3D Which of the following consumption streams will he choose? (Hint: there is no need to compute the utility function for each option. Just look at the tradeoffs between the immediate consumption and the future consumption.) (A) co = c1 = c2 = 10; 5, c1 = 15, c2 5, c1 = 10, c2 = 15; (D) co = 9, c1 = 10, c2 = 12. (B) co 10; (C) co %3D 19. Emma maximizes quasi-hyperbolic discounted utility U(co, C1, c2) = co+Bốc1 + B8?c2 for B = 0.5 and d = 0.8. Which of the following consumption streams will she choose? (A) co = C1 = c2 = 10; (B) co 5, c1 = 15, c2 10; (C) co = 5, c1 = 10, c2 = 15; (D) co = 9, c1 = 10, c2 = 12.
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- 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.…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.Please no written by hand solutions Data on before-tax income, taxes paid and consumption spending (on domestic goods and services) for the Simpson family in various years are given below. BEFORE-TAX INCOME ($) TAX PAID ($) CONSUMPTION SPENDING ($) 3000 3500 3700 4000 25 000 27 000 28 000 30 000 20 000 21 350 22 070 23 600 a. Graph the Simpsons's consumption function and find their household's marginal propensity to consume. b. How much would you expect the Simpsons to consume if their income was $32 000 and they paid taxes of $5000? c. Homer Simpson wins a lottery prize. As a result, the Simpson family increases its consumption by $1000 at each level of after-tax income. ('Income' does not include the prize money.) How does this change affect the graph of their consumption function? How does it affect their marginal propensity to consume?
- You are an economic advisor to the government. Discuss your opinion . a) How COVID-19 pandemic will affect the consumption behavior as well as the investment done by the firms and household for the next two years? b) What are the actions or policies that the government can implement to face this situation? please answers with analysis and --graph (if possible)Suppose your current income is $90,000 and your future income is $110,000. The interest rate is 10%. a. Suppose your optimal bundle is to live “paycheck by paycheck”, draw the intertemporal budget constraint and optimal bundle in a graph, and mark the optimal bundle and maximum C1, C2.b. What if your MRTP is 1.05, how should you change your consumption? c. What if your MRTP is 1.2, how should you change your consumption?d. If the interest rate decreases to 5%, how should you change your consumption? If the interest rate increase to 15%, how should you change your consumption?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’*?
- A consumer has utility u(x,y,z)= ln(x) + 2ln(y) + 3ln(z) over the three goods, x,y and z and pZ = 1 . Optimally sheconsumes 30 units of z. What is her income? How much money does she spend on x?(HINT: MUX =??, MUY =??, MUZ =??and remember the “equivalent bang for the buck” condition)(b) Forget about (a). Suppose you have t = 29 hours in total to spend on 3 projects X, Y and Z to make some money.If you spend x hours on project X, you make 2√? dollars;If you spend y hours on project Y, you make ?√? dollars;If you spend z hours on project Z, you make ?√? dollars;Writing down your “utility function” u(x,y,z) and the constraint, solve the utility maximization problem; what isthe optimal amount of time to spend on x ? on y? on z ?7 Consider a model in which an individual lives only two periods. This person has diminishing marginal utility of consumption and receives an income of $20,000 in period 1 and an income of $5,000 in period 2. The private interest rate is 10 percent per period, and this person can borrow or lend money at this rate. Also assume that this person intends to consume all of his income over his lifetime. a. Give a hypothetical numerical example of what a person’s optimal consumption would be over these two periods. In answering this question, what assumptions did you make?QUESTION 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…
- 2. Mr. A has the following utility function and budget constraints: Max 0.1Ln(C1) + 0.7Ln(C2) Subject to S1 + C1 = 100 C2 + S2 = (1 + r)S1 where C1 and C2 are consumption level at young and that at old respectively. Likewise, S1 and S2 are saving at young and saving at old respectively. a) Find out Mr. A’s optimal consumption levels (i.e. C1*, C2*) and optimal savings (i.e. S1*, S2*) in terms of interest rate r. b) Show clearly the results in part a) in a suitable diagram (with C1 as x-axis and C2 as y-axis). c) Is Mr. A a saver ? or a borrower ? d) If r is equal to 0 (i.e. saving gives no returns), will Mr. A still choose to save when he is young (i.e. is S1 still bigger than 0) ? Why ? e) Suppose that Mr. A is not allowed to save (i.e. S1 = 0). What are his optimal consumption levels ? Show his optimal consumption levels in the same diagram you prepare for part a) (with a suitable indifference curve). f) If r increases,…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 >…Suppose that a consumer/investor has an initial endowment only for the current period, which is Eo =450. She may consume today or in the next period only (two-period model). The interest rate for borrowing and lending in the capital market is 5% (a)Depict the budget constraint for the investor in an inter-temporal consumption diagram! What is the maximum amount the consumer is able to consume in the next period? (b)The consumption preferences of the consumer/investor are best described by a square root function, defined over current and future consumption. What is his optimal consumption plan? Show your calculations! Depict the results in appropriate diagram. Which amount is invested in the capital market?