The Baumol-Tobin Model of Money Demand Suppose a household earns monthly income of Y= 2500 €, which is automatically deposited in his bank account. The household earns i = 3% interest on the balance in his bank account. Each withdrawal from the bank account creates a nominal transaction cost of T=100€. The household spends all his income at a constant rate on consumption, which can only be bought with cash. a) Determine the optimal number of money withdrawals from the bank account. b) Determine the optimal average money holding of this household.
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- Lwando owns a delicatessen, namely Foodies Paradise. Lwando has determined that he needs R5 000 cash per day for customer transactions. Lwando has a choice between going to the bank first thing on Monday morning to withdraw R25 000 - enough cash for the whole week - or going to the bank first thing every morning for R5 000 each time. Lwando puts the cost of going to the bank at R6 per trip. Assume that funds left in the bank earn precisely enough interest to keep their purchasing power unaffected by inflation. Lwando's delicatessen is open 5 days a week for 48 weeks each year. If Lwando goes to the bank every day when the inflation rate is 5%, then the daily trips to the bank would result in net and Lwando's annual shoe leather costs of inflation equal_. Select one: a. loss of R652; R1 152 O b. savings of R652; R1 152 loss of R500; R1 440 d. savings of R500; R1 4401. Let's use the Euler equation two ways. First, to find out the optimal consump- tion path, taking the interest rate as given (Chapter 9 of GLS) and then to find out the equilibrium interest rate that wil Choose sidebar display for saving and investment, taking the consumption path as given (Chapter 11 of GLS). Both times, the utility function will be the same: Uln(c)+0.9ln(+1) So the future counts 90% as much as the present. In Part 1, income each period is 100, and the interest rate is 20%. In Part 2, consumption in each period is 100-in other words, income each period is 100, but income isn't storable (it's "manna"), so you have to consume it or lose it. Answer the following questions. Part 1: What is optimal consumption each period? In period t of this two- period world, will this person be borrowing or saving or neither? ⚫ Part 2: What is the equilibrium interest rate between these two periods? If the equilbrium interest rate were lower than that level, would that create a…5) Mrs. Gizem has a salary of 10000 TL per month. Assuming that her autonomous (zero-income level) consumption is 600 TL and her MPC is 0.72, find how much she spends in one month and how much she saves? b) If Mrs. Gizem receives a salary rise of 2000 which increases her monthly salary to 12 000 per month; how much increase we may expect in her consumption and her saving?
- 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.Using this functional form in the intertemporal trade-off condition that you previ- ously derived, do some algebra to obtain an equation that specifies how much the individual would save as a function of q, β, y1 and y2.1. According to the Bureau of Economic Analysis, during therecession of 2007–2009, household saving as a fraction of dis-posable personal income increased from a low of just over1 percent in the first quarter of 2008 to 5 percent in the secondquarter of 2009. All else equal, what impact would this changein saving have on the MPC, MPS, and multiplier? How wouldthis change affect equilibrium output when planned invest-ment changes? 2. Assume in a simple economy that the level of saving is –500 whenaggregate output equals zero and that the marginal propensity tosave is 0.2. Derive the saving function and the consumption func-tion, and draw a graph showing these functions. At what level ofaggregate output does the consumption curve cross the 45° line?Explain your answer and show this on the graph.
- 23. Guppse that fra,u)= T4. Find the maximum Value for fif x and y are constrained o sum to 1. Solve thiis problems in two ways : by substitutiou and by using the Logrange Multiplier method. X+y=1. F.y) =ry, 4=1-x. to -> %3D tx =-2x+1.maximum value → frx=o. X=E タニリニー 1-X-4 = 0 エ=f(Y,4)+A (1-g%-4) = x4ナA(1-%-4 ) = y-A, = x-1, of of 1-ベ-4 → 1-2y=0. X=立, %3D =0= y=X =07 X= À %3D #2-4. The dual problem to the one described in problem 2.3 is minimiz2e xty subject to xy =0.25 Solve thi problem using the Lagrangian technique. Then Compare the value You get tor the Logrange Multiplier wrth the value you got in Prolem 2-3. Explain the relatibuship between the two solutibnsConsider 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.)12. Given this diagram of Consumption and Savings functions, What will be the level of savings at an income level of 60? 6. Given this diagram of Consumption and Savings functions, What will be the level of savings at an income level of 20? 07. Given this diagram of Consumption and Savings functions, What is the level of total desired consumption at income level of 80? 8. Given this diagram of Consumption and Savings functions, What is the level of "induced consumption" at income level of 40
- The diagram depicts Marco's choice of consumptions in periods 1 and 2. He has $100 worth of grain in period 1 and no income in period 2. Marco decides to invest the entire amount of grain, which gives a return of 50%, and borrow against this future income at a 10% interest rate in order to consume $80 in period 1 (point A). Which of the following statements regarding his balance sheet is correct? Consumption later, $ 150 62 FF (invest grain; 50% return) FF (invest grain; 50% return; borrow at 10%) 80 100 Consumption now, $ 136 O The asset after borrowing but before consumption in period 1 is $100. The net worth before consumption in period 2 is $12. The net worth after consumption in period 1 is $20. The asset after consumption but before repaying the loan in period 2 is $80.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…Drive the is curve mathematically anf graphically when investment function is more sensitive to rate of interest