1) Sharon spends her time (20h) between leisure (L) and work and he consume Y product from his working income (Py=1). Assume that she gets W$ per hour of working and has the following utility function: U (L,Y)=LY+2L What will happen to L, Y and H if the wage per hour (W) will decrease? d. How would your answer to the previous question (c) will change if Sharon has a fixed amount of money (Wo) that is not connected to W? e. If Sharon has the following utility function: U= L³+ Y2, is it possible that she will choose not to work at all? Explain and
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- 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?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’*?Terry’s utility function over leisure (L) and other goods (Y ) is U(L, Y ) = Y + LY. The associated marginal utilities are MUY = 1 + L and MUL = Y. He purchases other goods at a price of $1, out of the income he earns from working. Show that, no matter what Terry’s wage rate, the optimal number of hours of leisure that he consumes is always the same. (a) What is the number of hours he would like to have for leisure? Determine the MRS of leisure for labour (b) Draw a leisure-influenced labor curve
- The consumer's utility function for Consumption (C) and Leisure (L) is given as U(C,L) = √CLHis hourly wage is $10, non-labor income is $20; and he has a total of 16 hours to allocate between labor and leisureBased on this information, the consumer's total utility at the optimal level (or optimal C,L combination) is:a. 57.0 utilsb. 28.5 utilsc. 99.75 utilsd. 114.5 utilse. Cannot be determined with the information given I prefer typed answers.Terry’s utility function over leisure (L) and other goods (Y) is U (L, Y) = Y + LY. The associated marginal utilities are MUY = 1 + L and MUL = Y. He purchases other goods at a price of $1, out of the income he earns from working. Show that, no matter what Terry’s wage rate, the optimal number of hours of leisure that he consumes is always the same. (a) What is the number of hours he would like to have for leisure? (b) Determine the MRS of leisure for labour (c) Draw a leisure-influenced labor curvei will 10 upvotes urgent Say Anna's utility function is given by UA = MAMM, where MA is Anna's wealth and MM is Marie's wealth. Initially, Anna has 160 units of wealth and Marie has 40. When Anna maximizes her utility, her utility level is equal to: Multiple Choice 10,000. 5,000. 100. 200.
- Joanna is playing blackjack for real money. She has reference-dependent preferences overmoney: if her earnings are m and her reference point is r, then her utility is v(m − r), wherethe value function v satisfies v(x) = √x for x ≥ 0, and v(x) = −2√−x for x ≤ 0a) Graph Joanna’s utility function as a function of m − rb) Does Joanna’s utility function satisfy loss aversion? Does it satisfy diminishingsensitivity?Suppose that Joanna has linear probability weights (that is, she does NOT have prospecttheory’s non-linear probability weighting function). Hence, if she has a fifty-fifty chance ofgetting amounts m and m′, and her reference point is r, her expected utility is1/2v(m − r) + 1/2v(m′− r) (2)For parts (c), (d), and (e), assume that Joanna’s reference point is $0 (that is, no winsor losses) and answer the following questions for each part: (i) What is the g for whichJoanna would be indifferent between not gambling and taking fifty-fifty win $g or lose$4 gamble? (ii) Does this reflect…This question will analyze the impact on a person's labour supply from a shock to their partner's job. Assume leisure is a normal good. Let's assume Vanessa has a wage rate of $20 per hour. Recently her partner, Bill, had to take a wage cut at work, with his wage falling from $45 per hour to $30 per hour, but allowed them to continue working 40 hours per week. Analyze the decision of the household over choice consumption and Vanessa's leisure, taking Bill's hours as given (constant).(Short Answers) 1. Jie works in a university. He can work as many hours as he wishes at a wage rate of w. Let C be the number of dollars he has to spend on consumption and let R be the number of hours of leisure that he chooses. Assume that Jie has the utility function U(C, R) = In(C) + In (R). He carms $4 per hour and has 80 hours per week to devote to labor or leisure, and has no income from sources other than labor. a) How many consumptions does he choose? How many hours of leisure does he choose? b) Suppose that Jie's wage rate will rise to $6 per hour from next year. How many hours of leisure per week will he choose next year? You are required to decompose his change in demand into the substitution effect, ordinary income effect and endowment income effect. c) Suppose that Jie will get $4 per hour for the first 35 hours that he works and $6 per hour for every hour beyond 35 hours a week from next year. How many hours of leisure per week will he choose next year?
- During any year, I can consume any amount that doesnot exceed my current wealth. If I consume c dollars duringa year, I earn ca units of happiness. By the beginning of thenext year, the previous year’s ending wealth grows by afactor k.a Formulate a recursion that can be used to maximizetotal utility earned during the next T years. Assume Ioriginally have w0 dollars.b Let ft(w) be the maximum utility earned during years t, t 1, . . . , T, given that I have w dollars at the be-ginning of year t; and ct(w) be the amount that should be consumed during year t to attain ft(w). By workingbackward, show that for appropriately chosen constantsat and bt,ft(w) btwa and ct(w) atwInterpret these results.James has a wage income of $50.000 in the present and $200.000 in the future. His utility is given as U = min (2Cp, Cr) - that is, his utility is the lesser of twice the dollars spent on present consumption or the dollars spent on future consumption. The interest rate is 30%. (A) What is the minimum amount of money James would be willing to accept today to have the interest rate at 40% rather than 30%? Explain and show work (B) What is the maximum amount of money James would pay today to have the interest rate at 30% rather than 40%? Explain and show workKhan lives in a world with two consumption goods x and y. Her utility function is U (x, y) = √x² + y². a. If px = $3,py = $4, and her income, I, is equal to $50, what will be the quantities of x and y that Maya should buy to maximize her utility? Make sure that you write out the Lagrangian and the first-order conditions. (Hint: It may be easier to maximize U² than U). Have you found a true maximum? Explain your answer.