Holly's utility function is U(c1, c2) = c21 + 0.87/22, where cį is her consumption in peric and c2 is her consumption in period 2. In perioc her income is twice as large as her income in period 1. At what interest rate will she choose to me the sOunt in poried in
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- John and Peter are two representative consumers/investors who maximize the utility of consumption. John's utility of consumption is characterized as ln(x) + 2ln(y) while Peter puts more weight on the current consumption level and has a utility function of 2ln(x) + ln(y). John has a wealth of ($10, $20) thousand, while Peter has a wealth of ($20, $15) thousand now and next year, respectively. (a) What are the optimal consumption plans forJohn and Peter,respectively,if the interest rate is 5% per annum? (b) If John and Peter are the only investors/consumers, what is the equilibrium interest rate? (c) Further to part (b), how much do they borrow or lend to each other?A university student was bequeathed $2,000 upon graduation at age 20 years. This person was hired by one of the largest global tech companies soon after graduation with an expected annual income of $250. Assume that the retirement age is 65 years and life expectancy is 85 years in the country in which the student resides. Given that this country has zero real interest rate and consumption smoothing is optimal for all individuals: Derive an expression for the person’s lifetime resources clearly describing each term. Calculate the value of the person’s lifetime resources. Derive an expression for the person’s consumption function clearly describing any new terms included. Derive an expression for the person’s average propensity to consuming. State the theory on which you based the calculations in parts i., ii. and iii. above.Suppose schmidt owns some land and is trying to decide when to sell it for a shopping center development. Her goal is to maximize her net worth, the present value of her other income stream plus the value of the land or the value of investment made with the proceeds of selling the land. The land is now worth $100k if sold. Suppose that the value of the land is expeted to increase at a rate that will slowly decrease over time as she waits. A.) Suppose schmidt expects the land to be worth $104k next year. Should she sell it now? Why? B.) If she expects it to be worth $110k in a year, should she sell now, Why? C.) At what next year land value would Schmidt be indifferent between selling and holding a year?
- Clare is contemplating her possible consumption patter for this year and next. She know that she will have income of $50,000 this year and $55,000 next yea. Her plan is to consume $40,000 this year (t=0). She is also going to invest 30,000. This investment has a positive NPV of $450. She decides to take the investment; in addition, the return on the investment is 9.62%. What consumption she can expect at t=1? (show a detailed procedure)Suppose an individual places his money in a bank for a year then invests in apples for a year. Suppose the bank has an annual rate of 5%, compounded continuously. During the year in which the individual's money is in the bank, the apple grows in price from $1 to $1.25. Suppose its return doubles in the second year, when the individual's money is invested in the apples. He starts the first investment period with $100. How much money does he have after two years following the investment plan given above? Group of answer choices $105.1 $124.7 $154.4 $157.7Suppose your utility function for money is a square-root function of its value in US dollars. So, for instance, $400 is worth 20 utils for you, $961 is worth 31 utils for you, and $62.5K is worth 250 utils for you. Now, let’s say your annual salary is $90K, although there is a small risk (p = 0.05) that something catastrophic will happen and reduce your income for the year to $14.4K. An insurance company comes along and offers to insure you against the loss of your salary. The cost of the insurance is $4,736. If you buy the policy and catastrophe strikes, the insurance company will pay out the $75,600 that you would otherwise have lost. From the standpoint of maximizing expected utility, would buying this insurance be a good deal for you? What would be the insurance company’s expected monetary value of selling you the policy?
- Amy is figuring out her budget for two periods, t∈1,2 . In each period, she has an income yt with y1=200 and y2=0 . ct denotes her consumption level at period t . Amy decides to spend half of her first period income immediately, so c1=100 , and invest the other half ( $100 ). Amy has two investment options. One option is to buy stocks from company B . Each share costs $1 at t=1 . At t=2, the stock price is uncertain. There is a 10 % chance the stock price increases to $4 per share, a 50 % chance the stock price increases to $2.25 per share, and a 40 % chance the company B goes bankrupt and the stock price falls to $0 per share. Amy's other option is to invest all $100 in a savings account. But at t=2 , there is also a random shock to the savings account. There is a 50 % chance the bank operates normally and the interest rate is r=44 % and a 50 % chance the interest rate falls to 0 (but Amy can still get her $100 principal back). 1. Assume without proof that at t=1 , she still consumes…Amy is figuring out her budget for two periods, t∈1,2 . In each period, she has an income yt with y1=200 and y2=0 . ct denotes her consumption level at period t . Amy decides to spend half of her first period income immediately, so c1=100 , and invest the other half ( $100 ). Amy has two investment options. One option is to buy stocks from company B . Each share costs $1 at t=1 . At t=2, the stock price is uncertain. There is a 10 % chance the stock price increases to $4 per share, a 50 % chance the stock price increases to $2.25 per share, and a 40 % chance the company B goes bankrupt and the stock price falls to $0 per share. Amy's other option is to invest all $100 in a savings account. But at t=2 , there is also a random shock to the savings account. There is a 50 % chance the bank operates normally and the interest rate is r=44 % and a 50 % chance the interest rate falls to 0 (but Amy can still get her $100 principal back). 1. If Amy invests $ 100 in stocks at t=1 , what is the…APPLIED ECONOMICS Topic: Intertemporal Choice Levinn’s utility function is expressed as the following: U= C1 C2 0.3 where C1 is his first periodconsumption and C2 is his second period consumption. His income in the first period is$2500 and interest rate is at 10%. If at equilibrium, Levinn is neither a borrower nor a lender,then what is his expected income in the second period? Show the graph if possible
- Assuming a mix of present and future consumption is preferred, ANY consumer who starts at point A will gain utility from a rise in interest rates. is it true or falseConsumers deposit their total saving, equaling the value of 1, at the bank at t = 0. The bank invests all deposit in an illiquid asset, yielding R = 1.5 inperiod 2 and has a liquidation value of 1 at period 1. Consumers have the probability of 25 percent of being impatient and consume in period 1. Theremaining patient consumers want to consume in period 2. The bank offers r(1) = 1.10 and r(2) = 1.20 as payment to consumers who withdraw inperiod 1 and period 2 respectively. Suppose that consumers believe at period 1 that 70 percent of the consumers withdraw their deposits at period 1, will this believe trigger a bankrun?APPLIED ECONOMICS Topic: Intertemporal Choice Levinn’s utility function is expressed as the following: U= C1 C2 0.3 where C1 is his first periodconsumption and C2 is his second period consumption. His income in the first period is$2500 and interest rate is at 10%. If at equilibrium, Levinn is neither a borrower nor a lender,then what is his expected income in the second period? Do not copy from others