3. Consider the individual's utility function: U = U(C, L) = L Ch (a) Compute the Marshallian labour supply. (b) Briefly discuss the main properties of this function.
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- (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?Brian uses wool (K) and labour (L) to produce t-shirts (q). The production function is: q = min{1/3L, 2K}. The inputs are perfect complement.If he uses 0.5 kg of wool and 3 hours of labour, he can produce 1 t-shirt. Draw an expansion path on a diagram and derive an expression for the expansion path. How does it depend on the wage and the price of wool?In the theory of consumer, we argued that the utility is ordinal, that is, utility number does not have any intrinsic meaning other than to give a preference ordering among consumption bundles. In other words, any increasing monotone transformation of a utility function represents the same preference, hence the spacing between indifference curves does not have any significance. Explain why in the theory of producer, the production function and the corresponding isoquant is a cardinal property, that is, the number itself has an intrinsic meaning. And explain the relationship between returns to scale and space between isoquants.
- Suppose the wage rate for labor is $20 an hour and the rental rate for capital is $50 per hour. Based on this information, please answer the questions appearing below the graph. 80 70 60 50 40 30 20 10 10 20 30 40 50 60 70 80 1,000 cases Labor Draw an (approximate) is-cost line associated with an hourly budget of $1,000. Hint: Find the intercept points first. If you were to shift this line out, what is the approximate least-cost combination of labor and capital when packaging 1,000 cases of fruit juice?- Find the marginal revenue function for the total revenue function given by 1 TR(Q) = 500Q Q3 - - 3 Find the marginal cost function for the total cost function given by TC(Q) = Q3 – 90Q² + 7,500QAn individual values both consumption and leisure. Suppose the individual has 1600 hours per week they can allocate between leisure and work. IF the individual works, they make a wage of $25 per hour. The individual's utility function is given as a function of leisure time, L and consumption, c: U(L, c) = L^(1/2)c ^ (1/2) a) Draw the individual's budget constraint for leisure and consumption. b) How much leisure time will the individual have when utility maximizing? c) Consider a Universal Basic Income policy like the one proposed by Andrew Yang that would give all individuals a lump -sum, unconditional cash transfer of $1,000 each month. How much leisure time will the individual have when utility maximizing with the cash transfer? d) Now suppose, instead of a cash transfer, a minimum wage of $40 per hour is implemented. How much leisure time will the individual have when utility maximizing with the cash transfer? e) What change in leisure time can be attributed to the substitution…
- Labor Market and Real Output: In the labor market, there is one representative worker and a representative firm. Worker supply hours of working (NS), and firm demand hours of work in order to produce output (Y). The production function that capture firm's production process is Y = f(N) = z√KN, where in the short run z=2 and K=100. Worker has a natural log utility function U(c, l) = In(c) + In(l). h=10, T T = 10. Please draw labor supply and labor demand in a graph and determine the equilibrium w*, N*, and Y*. If you cannot solve w*, N*, and Y*, you can just show where they are in the graph. (Note: MRS,c=and MPN: 2√N = Now, TFP (z) increases. What happen to the equilbirium outcomes (w*, N*, and Y*)? Please show it in an another graph. Are the changes the same as the example that we discussed in the class?Emma is employed at a contract where he can vary his labour supply between 0 and 40 hours per week. She derives utility from consumption, c, and leisure, L. Her preferences are represented by the following utility function: U(c,L) = min(c, L). The unit price of consumption is p, and the hourly wage rate is w. (a) Derive an expression for Emma's labour supply. (b) The government contemplates introducing a consumption boosting policy including a monthly transfer of money for which Emma is eligible. At what size of the transfer will Emma decide to not work? Assume that the unit price of consumption is 30 and the hourly wage rate is 50This 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).
- Construction workers in the town of Cortland, NY have Cobb-Douglas utility for labor and consumption, UL=(20-L)C, MRS=C20-L where L is the number of hours of labor supplied in a day and C is the dollar amount of consumption goods purchased with wage income (pc=$1 ). R=20-L is the number of hours of leisure that the worker has during the day. Derive the labor supply function for workers in Cortland. Draw the labor supply curve on a graph with L on the horizontal axis and w on the vertical axis.Suppose that following represents the utility function of the individual U(c,l)=log(c)+log(l) c = consumption level of the individual and l = leisure, while the market wage is 10 and available time is 20. 1) Find and draw the labor supply function. 2) Suppose that the government introduces a cash grant for the labor (who is in the labor force) in the amount of R. Find and draw the labor supply function? Compare it to the labor supply function you have found in a). 3) Discuss the existence of reservation wage in the settings described in a and b? If your answer is : “there are no reservation wages under those settings”, please introduce a change in the policy described in b) to make sure that the reservation wage would exist.Question 1 A firm wishes to produce to Q units of output using two inputs - ₁ and ₂. The prices of the inputs are w₁ and w₂ respectively. Assuming the firm wants to keep its current production target, show the effect on the firm's optimal input choice in a diagram if the price of factor x₁ increases. In a separate diagram, derive the conditional factor demand for input x₁, i.e., the relationship between price of x₁ and quantity demanded for ₁.