Consumer has utility function In(c1)+beta*In(c2), where beta=1. Interest rate i=0%. (NOTE!) Income y1=10 and y2=50. Gov't gives consumer a free stimulus check of $20 in the first period.
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- A person has a 2-period utility consumption function U(c1, c2), with a budget function W = c1+c2/1+ra. Explain with pictures how one should choose c1 and c2 such that MRS(from c1 to c2) equals 1+r.b. Also explain with pictures how when the individual receives income, whileconditions at that time was a crisis.Consumer has utility function ln(c1)+beta*ln(c2), where beta=1. Interest rate i=0%. (NOTE!) Income y1=10 and y2=50. Gov't gives consumer a free stimulus check of $20 in the first period. Assume consumers are sophisticated (have rational expectation), then in the first period the consumer will consume c1=______.Exercise 3 An individual lives two periods, 0 and 1. The income is 14,000 in period 0 and 5,000 in period 1. The individual's marginal utility is: K- Co in period 0 and d8(K – C1) in period 1, where C is the consumption in period 0, C1 the consumption in period 1 and d a discount rate. K is a constant (higher than the consumption in each period). Suppose that the person can save or borrow from the bank from period 0 to period 1 with a 25% interest rate. Set the discount rate & to 0.8. a) How much will the individual consume in the two periods? How much will she save? b) A National Insurance scheme (pension system) is established. The individual must pay 4,500 in period 0 and receives the same amount with interests in addition to her income in period 1. What will the consumption and savings be in the two periods if the National Insurance scheme uses the same interest rate as the bank?
- 6. A consumer who lives for two periods has a standard Cobb-Douglas utility func- tion: ule1, c2) = cfc, where c, = consumption in period t and a+ B = 1. Her income in period one is I1 = 500 and I2 = 400, and she can lend or borrow at interest rate r = 0.2. (a) Find the optimal consumption demand. (b) What values of a, if any, makes the consumer a borrower? Interpret this result. (c) Suppose now that a = but that r is no longer 0.2. What values of r, if any, makes the consumer a borrower? Interpret this result.2) Yoni spends his income on consumption between two periods C1 and C2. Both C1 and C2 are normal goods. Assume that in the initial position, Yoni's income in the first period is equal to his income in the second period. Yoni is indifferent between the present and the future and faces a convex utility function. The interest rate is equal to the inflation rate in the initial position. a. b. C. Draw Yoni's budget constraint and his optimal bundle. Point out C1 and C2 in the optimal bundle, the intercepts and the slope. Are Yoni's savings positive/negative/zero? Explain. What will happen to Yoni's utility if the inflation rate decreases and the interest rate increases? Point out the range of the new bundle.Suppose that y =100 (income today) • y' = 150 (income tomorrow) 10% (interest rate on bonds) %3D r = • t = 10 (taxes today) • t' = 10 (taxes tomorrow) Suppose that c = 100. Is the consumer borrowing or saving, today? And what will her budget constraint look tomorrow? The consumer is borrowing. Her budget constraint tomorrow will be c' = 150 -10 - 10*(1.1) = 129 The consumer is saving. Her budget constraint tomorrow will be c' = 150 -10 + 10*(1.1) = 151 O The consumer is neither borrowing nor saving - she is breaking even. Her budget constraint tomorrow will be c' = 150 -10 = 140 O The consumer is saving. Her budget constraint tomorrow will be c' = 150 + 10*(1.1) = 161 %D
- Help me1. Mia receives $100 of income this period and $100 next period. At an interest rate of 10 percent, he consumes all her current income in each period. He has a diminishing marginal rate of time preference between consumption next period and consumption this period. The interest rate rises to 20 percent. • Draw Mia's budget constraint, indifference curve, and label optimal bundle before and after the change in interest rate. o Will Mia save some of her income this period? Explain your answer in two sentences.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,…
- 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…Suppose the economy is characterized by the following behavioral equation: Y = C + I + G + (X-M) Equilibrium condition C = 2000 -f' 0.75Yd Consumption equation I = 4000 Investment expenditure G = 4100 Government Expenditure X = 2800 Export M = 400 + 0.25Y Import equation T = 100 + 0.3Y Tax equation Yd = disposable IncomeRequired: Derive Balance of Payment (BP) curve and explain why it slopes upwards Compute equilibrium national income and Imports for the economy. Differentiate between the closed-economy model and the open economy modelSeung's utility function is given by U - C^(1/2), where C is consumption and C^(1/2) is the square root of consumption. She makes $50,625 per year and enjoys jumping out of airplanes. There's a 5% chance that in the next year, she will break both legs, incur medical costs of $30,000, and lose an additional $5,000 from missing work. a. What is Seung's expected utility without insurance? b. Suppose Seung can buy insurance that will cover the medical expenses but not the forgone part of her salary. How much would an actuarially fair policy cost, and what is the expected utility if she buys it? Policy cost: $___ Expected utility: ___ c. Suppose Seung can buy insurance that will cover her medical expenses and foregone salary. How much would such a policy cost if it's actuarially fair, and what is her expected utility if she buys it? Policy cost: $___ Expected Utility: ___