Finite Horizon: Consider the following Planner's Problem: max (c₁k₁+1) s.t. : B'log (c) t=0 G+k₁+1= Aka, t= 0, 1, 2... C, kt+1 20, t= 0, 1, 2... ko> 0, given. (a) Suppose that A= 100, a 0.4, 3=0.9, ko 1 y T = 1. Compute the optimal capital level at t= 1. (b) Discuss how the steady state level of capital changes with 3 and A.
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- Title Suppose that Lynn enjoys coconut oil in her coffee. She has very particular preferences, and she mus Description Suppose that Lynn enjoys coconut oil in her coffee. She has very particular preferences, and she must have exactly two spoonfuls of coconut oil for each cup of coffee. Let C be the number of cups of coffee, and O be the number of spoonfuls of coconut oil. Also, let PC be the price of a cup of coffee. Suppose Lynn has $12 to spend on coffee and coconut oil. Also, the price of coconut oil is $.50 per spoonful.a) Graph Lynnâs Price Consumption Curve for prices, PC = $1, PC = $2, and PC = $3. Please put the number of cups of coffee on the horizontal axis, and the number of spoonfuls of coconut oil on the vertical axis. Be sure to label your graph carefully and accurately.b) Graph Lynnâs demand curve for coffee. You may assume that both coconut oil and coffee are continuous variables so she can consume any amount of coffee and coconut oil that she could afford.…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.…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 >…
- Q2. a. What is the law of demand? Give two examples of how you have observed the law of demand at work in the “real world.” How is the law of demand related to the demand curve?b. What variables influence the demand for a normal good? Explain why a reduction in the price of a normal good does not increase the demand for that good.Q4. What is econometric forecasting? If econometrics forecasting is considered the bestforecasting technique, what usefulness remains over other forecasting techniques2) Is the marginal utility of money income uniquely defined? 3) Examine the responses of an electricity consumer to changes in the connection charge and prices of electricity.18. Declining MRSXY implies that:(a) The total utility is decreasing along an indifference curve(b) The consumer’s preferences do not satisfy the more-is-better principle(c) The consumer is willing to give up more and more X for additional Y as the consumption of X increases along an indifference curve(d) The consumer is willing to give up less and less X for additional Y as the consumptionof X increases along an indifference curve
- Q. 1 You are the mayor of a small town with 2000 residents. The head of your economic development agency recently conducted a survey in which the 2000 residents said that a public concert in the centre of town would be worth $20 to cach of them. Since it costs only $5000 to hold the concert, you organized and held the concert, which everyone in town enjoyed. But when you asked for donations to pay for the concert, you only collected $30 in total. What do you know? a. The survey certainly overstated how much the concert was worth to each resident. b. From the standpoint of total costs and benefits, the cost of the concert certainly exceceded the benefit. c. The concert was an example of the Tragedy of the Commons. d. Residents of the town were probably free riders.3. Suppose that individuals with a strong enthusiasm for technology are willing to pay $500 now for the latest iPhone, but only $350 if they must wait a year. Normal people are willing to pay $250, and their desire to purchase does not vary with time. Assume for simplicity that there are equal numbers of each customer type (strong enthusiasm and normal), that the MC of the iPhone is $100, ignore the time value of money, and there are only two years. (Hint: With discrete problems consider all the different options and evaluate each of them to determine the optimal strategy. In this case, there are only three prices given and two time periods, so a total of 6 pricing strategies exist but some of them will.) What is the highest profit level that can be achieved if the price for an iPhone is fixed for both years (uniform pricing)? What is the highest profit level that can be achieved if the price for an iPhone can be altered across the two years?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.
- 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,…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 lenders