der a two-period living consumer with a utility function, u(c)=sqrt(c). Suppose the real interest rate, R=10% and the utility discount factor, beta=0.95. If the consumer wants to maximize lifetime utility, what will be the growth rate of her consumption from the current to the future period?
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Consider a two-period living consumer with a utility function, u(c)=sqrt(c). Suppose the real interest rate, R=10% and the utility discount factor, beta=0.95. If the consumer wants to maximize lifetime utility, what will be the growth rate of her consumption from the current to the future period?
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- Consumer's utility function for consumption in two periods is c1+30ln(c2). The interest rate is r, the income in the first period is 10, the income in the second period is 50. What is the formula for the demand for second-period consumption?A family of four has an income of $15,000 today and will earn $24,000 tomorrow. If the family consumes $11,500 in the first period and $15,000 in the second period what is the interest rate?Suppose interest rate is 10 % and consumer's utility function is given by U(C1,C2)=C1C2. Income in the first period is 100 and income in the second period is 121. a) Find optimal consumption is each period. b) Does the consumer borrow? In which period? How much? c) Show the answers on a diagram.
- Consider the household model that you have seen in class but now assume that the goal of the household is to consume twice as much in period 2 as in period 1. She earns $100 in the first period and $150 in the second period. The interest rate is 5%. What is her optimal saving in the first period? Note: Type in your answer approximated to two decimal points, i.e., your answer must be of the form "999.99". I will not be able to fix correct answers that were entered incorrectly, such as "999.999" or "999,99" or "999". In case the last digit in the correct answer is zero, e.g., "999.90" or "999.00", Blackboard will automatically delete it and you should not do anything about it.Define time preferences for consumptionAssume a consumer has current-period income y = 200, future-period income y′ = 150, current and future taxes t = 40 and t′ = 50, respectively, and faces a market real interest rate of r = 0.05, or 5% per period. The consumer would like to consume according to the following utility function: U (c, c′ ) = ln(c) + ln(c′ ). Show mathematically the lifetime budget constraint for this consumer. Find the optimal consumption in the current and future periods and optimal saving. Suppose that instead of r = 0.05 the interest rate is r = 0.1. Repeat parts (a) and (b). Does the substitution effect or the income effect dominate?
- 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 $157.7it is given that the ratio of APS to APC is 2/7 Calculate the ratio of Consumption to savingsAn individual derives utility from consumption spending C and leisurel according to the following utility function: U(C,1)=C 1¹-a where 0>a>1. Leisure time in hours is given by: 1=T-H where T is hours of total time available and H is hours of work. The consumer's real income is given by: C=w (T-1)+N where w is real wage and N is real non-labour income. b) In which situation would the individual's supply of hours of work be independent of the hourly wage rate w?
- Consider the two period consumption savings problem faced by an individual whose utility is defined on period consumption. This utility function u(c) has the properties that it is strictly increasing and concave, u'(c) > 0, u"(c) < 0 (where u'(c) denotes the first derivative while u"(c) represents the second derivative) and satisfies the Inada condition lim.-→0 u'(c) approaches zero). The individual's lifetime utility is give by u(cı) + Bu(c2). In the first period of life, the individual has y1 units of income that can be either consumed or saved. In order to save, the individual must purchase bonds at a price of q units of the consumption good per bond. Each of these bonds returns a single unit of the consumption good in period 2. Total savings through bond purchases is s1 so that total expenditures on purchasing bonds is qs1. Let c1 denote the amount of consumption in period 1 chosen by the individual. In the second period of life, consumption in the amount c2 is financed out of the…In Irving Fisher’s two period model, if the consumer is initially a saver and the interestrate and the first period consumption increases, then we can conclude that the incomeeffect:a) Was greater than the substitution effectb) Was less than substitution effectc) Exact offset the substitution effectd) And the substitution effect both increased consumptionAn individual derives utility from consumption spending C and leisurel according to the following utility function: U(C,1)=C"1¹-a where 0>a>1. Leisure time in hours is given by: 1=T-H where T is hours of total time available and H is hours of work. The consumer's real income is given by: C=w (T-1)+N where w is real wage and N is real non-labour income. d) Verify that the second-order conditions for a constrained maximum are met. Reduce your answer (which should only be function a, w, N, and T) to the lowest terms.