Consider the utility function of a worker who allocates his available daily time (T) to work(H) and leisure (L) as U-Y'+ L'obtains his total income (Y) from both Jabour and non-labour sources as Y = wH +v where vis remittances received from abroad.where Y is income and L is leisure. The workermarks)B marks)(a) Derive the worker's demand function for Leisure (L*).(b) Determine his labour supply function (H*).(c) What is the relationship between Hours of work (H*) and remittances received fromabroad (v)? (a) Given the Cournot aggregation for two commodities as a, (e,, +1)+a,E-0 wherea1 and az represent the budget shares of commodities 1 and 2 respectively; ell is ownprice elasticity of commodity 1, and E21 is the cross price elasticity of commodity 2with respect to price of commodity 1. If the own price elasticity of commodity 1 is -2 and the consumer spends 40% of his income on commodity 1, compute the crossprice elasticity of commodity 2 with respect to the price of commodity 1 and indicatethe relationship between the two commodities.(b) Consider total expenditure on a commodity as TE = pq . Show that for a fairly eiasticdemand for the commodity, an increase in price of the commodity results in adecrease in consumer's total expenditure.(c) The short-run production function of a Farmer is given by q = 6le-le where a istotal output; I is land input and e is labour input represented by number of workersengaged on the farm. Assuming land is fixed at 5 hectares, determine thenumber of workers engaged on the farm that captures the relevant region of thisrange of therational farmer.

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Consider the utility function of a worker who allocates his available dalny (H) and leisure (L) as U-Y'+L obtains his total income (Y) from both labour and non-labour sources as Y = wH +v where v is remittances received from abroad. where Y is income and L is leisure. The worker (a) Derive the worker's demand function for Leisure (L*). (b) Determine his labour supply function (H*). (c) What is the relationship between Hours of work (H*) and remittances received from abroad (v)?

Consider the utility function of a worker who allocates his available dalny (H) and leisure (L) as U-Y'+L obtains his total income (Y) from both labour and non-labour sources as Y = wH +v where v is remittances received from abroad. where Y is income and L is leisure. The worker (a) Derive the worker's demand function for Leisure (L). (b) Determine his labour supply function (H). (c) What is the relationship between Hours of work (H*) and remittances received from abroad (v)?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Consider the following labor-leisure choice model. Utility function over consumption (C) and leisure (L) U(C.L) = (1/3L1/3 Total hours: H = 40 Labor hours: NS = H - L Non-labor income: π = 30 Lumpsum tax: T = 10 Hourly wage: w = 4 Suppose the hourly wage changes to w = 3. What is the substitution effect of this change on labor supply? A. +2.65 B. -2.65 C. +3.48 D.-3.48 E. None of the above
Akua gains utility from consumption C and leisure L. The most leisure she can consume in any given week is 110 hours. Her utility function is U (C, L) = C × L. Akua receives 660 GHS each week from her great-grandmother—regardless of how much she works. a. What will be Akua’s marginal rate of substitution. b. What will be Akua’s reservation wage? (Explain in detail)
2. Let an individual’s utility function be given by where C and L are consumption and leisure respectively, and g, a and b are positive constants with a + b = 1. Derive the individual’s Marshallian labor supply function and comment on the magnitudes of the income and substitution effects of wage change. Derive the general form of Slutsky equation of labor supply.
(i) Keith’s marginal utility of leisure is C – 20 and his marginal utility of consumption is L – 50. There are 110 hours in the week available to split between work and leisure. Keith receives £250 of welfare payments each week regardless of how much he works (assume he spends all of his welfare payments on consumption). What is Keith’s reservation wage? (ii) Suppose Danny receives the same welfare payments each week as Keith and has the same number of available hours (110). However, Danny’s indifference curve is flatter than Keith’s. How would his reservation wage compare to Keith’s? Why?
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1) What would be the substitution effect and the income effect of a wage increase? 2) What do you think accounts for the wide range of savings rates in different countries
Suppose that the utility function of an individual is given by U=YL2, where Y is real income and L is leisure time. The marginal utilities are MUL =0.5YL-1/2 and MUy=0.5Y-12L1/2 There are 15 hours available for labour/leisurer the current wage rate is $20 per hour, and the price index for real income is 5. Assume that there is no non-labour income. Show minimal calculation work. a) Determine the budget constraint function? b) Determine the optimal relationship between income and labour hours? C) Calculate the optimal amount of labour hours? d) Calculate the optimal amount of leisure hours? e) Calculate the income level of the individual at the optimal condition? - Calculate the utility level for the individual at the optimal condition?
The following utility function represents Rose's preference over consumption and leisure u(c, l) = √c + 4√l. Rose receives a real wage of 15 and a non-wage income of 2. As a qualified recipient, Rose gets an additional non-wage income of 5 from the government through a cash transfer program. What is Rose's optimal choice of labor supply?
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Refer to the following diagram. Point A is 24 hours, C is 14 hours, D is 8 hours, and E is 6 hours. Income B₂ 0 D -Leisure If the current wage rate results in a budget constraint of AB2, how many hours will the individual work?
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This problem considers the decisions of a consumer whose preferences are given by u(C,1)=C+4 lnl, in which C' is the quantity of consumption and I is the quantity of leisure. The consumer faces two constraints. The time constraint is given by 1 + N³ = 1 with NS as the time spent working (or the labor supply). The main advantage of working is the wages consumers receive. Consumers take wages as given (outside of their control) and obtain wage income equal to wN³. The budget constraint is C wNsT, with π as real dividend income and T as the real = lump-sum taxes paid to government.