1. An individual derives utility from the consumption of a basket of goods, c and leisure time, & given by U(c₂l) = cºl(¹-a) where 0 < a < 1, is a constant; and must decide how to allocate her time between work, L and leisure to maximize her utility. The individual has a total of 24 hrs in a day (L + l = 24) and total consumption is constrained by her income; i.e., c = wL, where w the real per hour, is taken as given.
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- QUESTION 1An individual lives for two periods and decides how much to consume in each period.- In the first period his consumption equals C1 and his income Y1 = 200- In the second period his consumption equals C2 and his income Y2 = 100He can save or borrow money in the first period to finance his consumption in the second period.The interest rate he gets in case he saves or has to pay in case he borrows money equals 7%.Determine the budget constraint of this individual. C2 = −0.935·C1 +314C2 =−1.07·C1 +314C2 =−0.8·C1 +314C2 =−1.08·C1 +314 QUESTION 2The total production of a good y is determined by the production function y = 3L2/3K1/3, where L is labour input and K capital input.The reward (factor prices) for labour and capital are, l = 27 en r = 2, respectively.The producer needs to produce 9000 units of good y.How much units of labour will he hire if he wants to miminize his total costs? 1587,4839,953000515,23 QUESTION 3A good is traded on a perfectly competitive…You are an economic advisor to the government. Discuss your opinion . a) How COVID-19 pandemic will affect the consumption behavior as well as the investment done by the firms and household for the next two years? b) What are the actions or policies that the government can implement to face this situation? please answers with analysis and --graph (if possible)Need help on part (d) and (e) 6. Assume you can work as many hours you wish at £12 per hour (net of tax). If you do not work, you have no income. You have no ability to borrow or lend, so your consumption, c, is simply equal to your income. a) Derive and plot the feasible set, between daily values of consumption c, and “leisure”, l. Label the values at the intercepts (the points where the feasible frontier cuts the two axes). b) Assume that your optimal choice of consumption and leisure is to work 8 hours per day. Illustrate this choice diagrammatically using the feasible set and indifference curves. c) Use indifference curves and the feasible set to show why, given the properties of the optimal choice in part b), it is not optimal to work, say, 10, or 6 hours per day. d) Now assume that you receive an income of £140 per week from an unknown benefactor. Show the impact on your feasible set, and show a new optimal choice in which consumption increases but labour supply decreases.…
- Q 1 5. Refer to the following intertemporal budget constraint of a respective consumer: a. How would this budget constraint change if individual becomes more presented oriented (he discounts future heavily)? b. How would this budget constraint change if individual faces a borrowing constraint in second period?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.)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’*?
- 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?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,…Tom's income is 32. He consumes a single consumption good, C, which has a price of 2. His utility function depends on his marital status: when happily married, his utility is given byU=C^(1/2) When he is not married, his utility is given by U=0.5C^(1/2) a. Suppose that Tom is not currently married. What is his utility? Now suppose that Tom gets married.What is his utility? Assume Tom can spend all his income on his own consumption when he is married. b. Use compensating variation (CV) and equivalent variation (EV) to calculate the value of marriage to Tom. How do the two figures compare?
- Suppose that a consumer/investor has an initial endowment only for the current period, which is Eo =450. She may consume today or in the next period only (two-period model). The interest rate for borrowing and lending in the capital market is 5% (a)Depict the budget constraint for the investor in an inter-temporal consumption diagram! What is the maximum amount the consumer is able to consume in the next period? (b)The consumption preferences of the consumer/investor are best described by a square root function, defined over current and future consumption. What is his optimal consumption plan? Show your calculations! Depict the results in appropriate diagram. Which amount is invested in the capital market?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?Remember to illustrate diagramatically for some of these parts! 6. Assume you can work as many hours you wish at £12 per hour (net of tax). If you do not work, you have no income. You have no ability to borrow or lend, so your consumption, c, is simply equal to your income. a) Derive and plot the feasible set, between daily values of consumption c, and “leisure”, l. Label the values at the intercepts (the points where the feasible frontier cuts the two axes). b) Assume that your optimal choice of consumption and leisure is to work 8 hours per day. Illustrate this choice diagrammatically using the feasible set and indifference curves. c) Use indifference curves and the feasible set to show why, given the properties of the optimal choice in part b), it is not optimal to work, say, 10, or 6 hours per day. d) Now assume that you receive an income of £140 per week from an unknown benefactor. Show the impact on your feasible set, and show a new optimal choice in which consumption increases…