Consider a household with a wealth endowment of $5, and a MB of consumption of $1.71, 1.53, 1.39, 1.29 and 1.23 for 1st, 2nd..... unit of consumption C. A firm faces MR at $1.66, 1.52, 1.42, 1.34 and 1.28, for the 1st, 2nd..... unit of capital, K. In this market, if the interest rate is 41%, then the demand for funds is units and the supply of funds is units. 02:2 O 2:3 O 3:3 O 3: 2
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- kal.4 An investor with an initial endowment of $ 16,000 is confronted with the following productivity curve: C1= 240 (16,000 − C0)0.5 where C0 denotes consumption at present, and C1 consumption in the future. Assume the interest rate (for borrowing and lending) is 20%. The investor's utility function, from which it is possible to derive his indifference curves, is defined as: U(C0, C1) =C0C1 . What is the NPV of the investment chosen by the investor?Consider an otherwise standard Arrow Debreu Equilibrium with some modifications. Suppose that households now are not allowed to own capital directly. Instead, firms own all of the initial capital stock ko and also make all future investments in capital. Households own all shares of the firms, and returns to the firms now include returns to capital. Make necessary changes to the firm's and the household's problems to fit the new arrangement, define the new equilibrium, and show that the equilibrium quantities and prices are same as before.Suppose that there are only 10 individuals in the economy each with the following utility function over present and future consumption: U (c1, c2) = c1 +C2, where ci is consumption today, and c2 is consumption tomorrow. Consumption tomorrow is less valued because people are impatient and prefer consuming now rather than later. Buying 1 unit of consumption today costs $1 today and buying 1 unit of consumption tomorrow costs $1 tomorrow. All individuals have income of $10 dollars today and no income tomorrow (because they will be retired) but they can save at the market interest rater> 0. How much of his or her income will an individual consume today given that the interest rate is 0.3? O. Less than half of it O. Exactly half of it O. The individual is indifferent between consuming today and saving O. More than half of it O. All of it O. None of it How much of his or her income will an individual consume today given that the interest rate is 0.5? O. Less than half of it…
- H1. Suppose an individual has a utility function U = C+3L, where C is the consumption level and L is the leisure hours. Suppose the individual has 100 hours in total for work and leisure and $10 non-labor income. The wage rate is $3.14. Which feasible consumption level maximizes the individual’s utility? (a) 0 (b) 1.8 (c) 9.42 (d) 10 (e) 31.4 (f) 96.86 (g) 100 (h) 131.4 (i) 314 (j) 324 (k) 414Elroy Harris is considering whether to buy a corn and soybean farm in Iowa. The farm will cost $800,000, and Xander will be able to pay this from profits his recently deceased mother made on the stock market and willed to him. He estimates that if he does not run the farm, and keeps his current job as an economic forecaster, he will be able to earn $40,000 a year. The prevailing interest rate is 9 percent. Xander’s only motive is to maximize his income. His accountant tells him the annual profit from the farm is likely to be depending on certain conditions and assuptions: Scenario i) $160,000 of accounting profit Scenario ii) $100,000 of accounting profit Scenario iii) $50,000 of accounting profit Using the concept of positive economic profit, which of the three scenarios would the economic opportunity cost justify him taking up farming and quitting his job as an economic forecast. Show your work and calculationsAssume 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 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.)Assume an individual has a utility function of this form U(C, L) = 20 + 4(C*L)1/2 This utility function implies that the individual’s marginal utility of leisure is 2(C/L)1/2 and her marginal utility of consumption is 2(L/C)1/2. The individual has an endowment of V=$80 in non-labour income and T = 16 hours to either work (h) or use for leisure (L). Assume that the price of each unit of consumption good p=$1 and the wage rate for each hour of work w=$10. a. How much utility does the individual receive if she consumes C = 100 and works h = 7 hours? b. Calculate the rate at which the individual is willing to sacrifice an additional leisure hour when she is already working 4 hours. c. What is this individual’s optimal amount of consumption and leisure?Assume an individual has a utility function of this form U(C, L) = 20 + 4(C*L)1/2 This utility function implies that the individual’s marginal utility of leisure is 2(C/L)1/2 and her marginal utility of consumption is 2(L/C)1/2. The individual has an endowment of V=$80 in non-labour income and T = 16 hours to either work (h) or use for leisure (L). Assume that the price of each unit of consumption good p=$1 and the wage rate for each hour of work w=$10. a. What is this individual’s optimal amount of consumption and leisure? b. Assume a cash grant welfare program is instituted which pays M = 20 dollars for individuals who do not work. Compute the new optimal labour supply for this individual under the welfare program. Assume that prior to the welfare program, p =$1, w =$10, and V =$80 (as in part c). Does the individual accept the welfare program and not work? Show why or why not.
- Consider the Two-Period Endowment Model of the Household studied in class. Suppose that optimal consumption period is given by: where ωe is the household's lifetime wealth (after taxes). Is the optimal consumption behaviour implied by (1) consistent with the Permanent Income Hypothesis? Why?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’*?Find the value of marginal efficiency of capital if the supply price is $10 in the prospective yield is $5?