plogy represe by the production function y =VL where y denotes coconuts and L denotes hours of labour. His preferences can be represented by the utility function u coconuts and R leisure. Robinson has an endowment of 12 hours to spend per day where R+ L= 12. The Pareto efficient allocation for Robinson is L= (numeric) and y= marginal rate of substitution to the marginal product of labour and use the production function and resource constraint for labour and leisure). yR where y denotes (numeric, rounded to two decimals). (Hint: equate the Blank # 1 Blank # 2
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- Ivan faces a labor supply decision. His well-behaved preferences over the two goods "hours of leisure' L and 'consumption' c can be represented by u= 4(L)1/2 +c. He has no non-labor income and can choose how many hours to work at the wage rate u per hour. The price per unit of consumption is p, and his available free time is T hours .a)Sketch Ivan's budget set, with axes, intercepts, and slope labeled (these will depend on the parameters w, p, and T) .b)Use the tangency method to find Ivan's demand functions for leisure and consumption (as functions of u, p. and T) .c) Let's think about Ivan's "time expansion path" (that is, the analog of the income expansion path a.k.a. income-consumption loci but for changes in T). Sketch it and explain why it has this shape. with reference to Ivan's demand functions.d) (3 points) In terms of parameters from the model, what is the most that Ivan would be willing to pay to have an extra hour of free time (that is, to increase T by 1)? Why?Ivan faces a labor supply decision. His well-behaved preferences over the two goods "hours of leisure' L and 'consumption' c can be represented by u= 4(L)1/2 +c. He has no non-labor income and can choose how many hours to work at the wage rate u per hour. The price per unit of consumption is p, and his available free time is T hours .a) Sketch Ivan's budget set, with axes, intercepts, and slope labeled (these will depend on the parameters w, p, and T) .b) Use the tangency method to find Ivan's demand functions for leisure and consumption (as functions of u, p. and T) .c) Let's think about Ivan's "time expansion path" (that is, the analog of the income expansion path a.k.a. income-consumption loci but for changes in T). Sketch it and explain why it has this shape. with reference to Ivan's demand functions.d) In terms of parameters from the model, what is the most that Ivan would be willing to pay to have an extra hour of free time (that is, to increase T by 1)? Why?Firzaowns 3 iced milk coffee bottlesand 9 toasted bread while Razi owns 8 iced milk coffee bottles and 4 toasted bread. Given this resources, marginal rate of substitution (MRS) toasted bread and milk coffee for Firza and Razi is 4 and 2, respectively. DrawEdgeworth box diagram and explain whether the resource allocation between Firza and Razi is efficient. If this allocation is inefficient, explain what should Firza and Razi substitute to obtain higher utility?
- Consider Alexei who makes $1,400 per week and just won a ‘set for life’ lottery ticket whichinvolves a fortnightly payment of $10,000 for 20 years. Currently he works 35 hours per week. Nowdo the following:• Illustrate the effect of the lottery win on Alexei’s budget constraint using a fully labelleddiagram where i) the horizontal axis represents the hours of free time per week, and ii) thevertical axis represents Alexei’s weekly consumption.• Illustrate on the same diagram Alexei’s optimal decisions before and after the lottery winalong with his indifference curves.Consider Justin who makes $1,400 per week and just won a ‘set for life’ lottery ticket whichinvolves a fortnightly payment of $10,000 for 20 years. Currently he works 35 hours per week. Nowdo the following: • Illustrate the effect of the lottery win on Justins budget constraint using a fully labelleddiagram where i) the horizontal axis represents the hours of free time per week, and ii) thevertical axis represents Justins weekly consumption. • Illustrate on the same diagram Justins optimal decisions before and after the lottery winalong with his indifference curves. • Based on your diagram, discuss whether Justin will quit his job.Is the marginal rate of substitution is another way to mathematically expressing the opportunity for one more unit of a good that is consumed
- Consider the production problem discussed in class in which 24 labor hours and 4 machinehours are to be allocated between food (x) production and wine (y) production. Suppose theproduction functions for x and y are as follows:Also, suppose the preferences of the agents are given by:Finally, suppose the MRT is given bywhere x and y denote, respectively, the aggregate quantities of food and wine produced.For each of the following allocations, determine whether they are (i) feasible and (ii) Paretoefficient. If they are inefficient, explain intuitively how it is possible to make someone betteroff without making the other person worse-off.a. ((14,2),(10,2),(5,10),(23,18))b. ((8,2),(16,2),(5,14),(11,18))c. ((14,2),(10,2),(14,21),(14,7))Trey works as a waiter for Puff & Stuff catering for a wage of w 11. In addition to his %3D labor income from waiting, Trey makes supplemental income with his household production time by streaming video games on Twitch. He doesn't have any unearned income (V=0). Trey's preferences over consumption and household production are given by the utility function below: u (H, C) = 2\H + VC Assume Trey has 16 hours each day to split between household production and consumption, if he spends 10% of his time at home streaming and earns an hourly rate of P = 7, what will be his optimal allocation of household production? (hint: assume that Trey's utility-max condition remains unchanged and his supplemental income will only impact his budget constraint)(a) Explain with the help of a graph the effect of an increase in the relative price of a labor-intensive good on input choice. (b) “Generally, an economy will tend to be relatively effective atproducing goods that are intensive in the factors with which the country is relatively wellendowed.” Explain the above statement with the help of a graph.
- Consider a worker whose choice is between hours of free time and consumption. His company has now cut his wage rate. Which of the following statements is correct? O As a result of the substitution effect, the worker would reduce his free time. The income effect means that the worker would increase his free time. The worker may or may not reduce his free time as a result of the wage cut. The income effect will always dominate the substitution effect of the wage cut.In this particular example, what are the contributions of the income and substitution effects?The diagram shows a student's indifference curves for hours of free time per day and final grade. Based on this graph, which of the following statements is correct? Final grade 100 84 75 0 E B 15 16 Hours of free time per day H 19 20 24 For a given final grade, the student's marginal rate of substitution between free time and final grade is the same on all three indifference curves. The marginal rate of substitution at B is smaller than 9. The marginal rate of substitution at H is 0.25. The marginal rate of substitution is higher at D than at A.