eek. We carns $1,000 each week and earns a real interest rate of p = 0.01 on any money ved today. He also needs to pay the same interest rate if he borrows money today and pays it next week. If his utility function is U (C₁, C₂) = c₂, where c₁ is units of consumption day and c₂ is units of consumption next week, how many units will he consume this week?
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- Suppose you have a monthly income of $1000, $850 in monthly expenses, and you can put money in a savings account that yields a monthly interest rate of 4%. Now suppose you have an opportunity to invest your money at a 12% return. Further suppose you are able to borrow at 3%. Assuming you invest all of your money and then borrow against your future payout, show your trade-off between present and future consumption. If you still need to consume $850 in the present, how much will you have to spend in the future?7 Consider a model in which an individual lives only two periods. This person has diminishing marginal utility of consumption and receives an income of $20,000 in period 1 and an income of $5,000 in period 2. The private interest rate is 10 percent per period, and this person can borrow or lend money at this rate. Also assume that this person intends to consume all of his income over his lifetime. a. Give a hypothetical numerical example of what a person’s optimal consumption would be over these two periods. In answering this question, what assumptions did you make?5. Suppose interest rates are zero and the consumer's utility is u(c_{1}, c_{2}) = (c_{1}, c_{2}) while the two incomes are (y_{1}, y_{2}) = (75, 125) . Find the optimal consumption in each period , and also indicate what financial transactions the consumer makes . Show the answers on a diagram .
- 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 lendersAssume that Abdullah has RO 44 to spend on Energy drinks and Protein Bars each month and that both goods must be purchased whole (no fractional units). Energy drinks cost RO 8 and Protein Bars cost RO 3 each. Abdullah’s preferences for Energy drinks and Protein Bars are summarized by the following information: Energy drinks Protein Bars No. per Month TU MU MU/Px No. per Month TU MU MU/Py 1 42 1 18 2 78 2 33 3 108 3 45 4 132 4 54 5 150 5 60 6 162 6 63 7 168 7 66 Fill in the figures for marginal utility and marginal utility per dollar both Energy drinks and Protein Bars. Are these preferences consistent with the law of diminishing marginal utility? Explain briefly. Given the budget of RO 22, what quantity of Protein Bars and what quantity of Energy drinks will maximize Joe’s…
- 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.…Suppose a consumer has $1500 in the current time period and $1100 in the future time period.Suppose also that the consumer can borrow and lend freely and, unless otherwise specified, borrowing and lending interest rates are the same. (a) If the interest rate between time periods is 50%, what is the budget constraint between consumption in the present and consumption in the future? (B) If the interest rate at which the consumer can borrow is 75% but the rate at which she can lend is25%, what is the budget constraint? (C) Suppose the interest rate is 50%. If the consumer has to pay a fee of 10% of the loan amount in order to borrow money, what is the budget constraint?Anya has a two-period horizon. She has the utility functionu (c1,c2) = 2ln(c1) + ln(c2), where cj is her consumption in period j. Her income is Mj in period j. Assume that M1= 7,000 and M2=9,600. The interest rate at which she can borrow and lend is 20%. (i) Find the equation for Anya’s budget line. (ii) Find her optimal bundle. (iii) Explain whether her utility would rise or fall if the interest rate were to fall slightly. (iv) Now suppose that the interest rate is again 20% and Anyahas M1= 0 and M2= 18,000.Explain why her optimal bundles here and in (ii) are related as they are. *just answer part iv.
- Anya has a two-period horizon. She has the utility functionu (c1,c2) = 2ln(c1) + ln(c2), where cj is her consumption in period j. Her income is Mj in period j. Assume that M1= 7,000 and M2=9,600. The interest rate at which she can borrow and lend is 20%. (i) Find the equation for Anya’s budget line. (ii) Find her optimal bundle. (iii) Explain whether her utility would rise or fall if the interest rate were to fall slightly. (iv) Now suppose that the interest rate is again 20% and Anyahas M1= 0 and M2= 18,000.Explain why her optimal bundles here and in (ii) are related as they are.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 40A college professor is planning for his retirement years. His utility function is ?(?t , ?r ) = 3c t 0.5+2cr0.5 where ct represents his consumption today (period 1), his active years of teaching, and cr represents his consumption in his retirement years (period 2). During his active years of teaching, he makes a total of ₺3 million, while in his retirement years his total income is ₺1 million. He can borrow or lend at an interest rate of 25% between the two periods. Write an equation that describes the professor’s budget assuming he will spend all his income during his lifetime. If the professor chooses neither to borrow nor to lend during his active years, what will be his marginal rate of substitution between his consumption today and his retirement years? If the professor aims at maximizing his utility, how much does he consume in each period (use the Lagrangian method)? Does he save for his retirement years? If so, how much? At what interest rate would the professor…