Assume an individual has a utility function of this form                                     U(C, L) = 20 + 4(C*L)1/2 This utility function implies that the individual’s marginal utility of leisure is 2(C/L)1/2 and her marginal utility of consumption is 2(L/C)1/2.  The individual has an endowment of V=$80 in non-labour income and T = 16 hours to either work (h) or use for leisure (L). Assume that the price of each unit of consumption good p=$1 and the wage rate for each hour of work w=$10.   a. What is this individual’s optimal amount of consumption and leisure? b. Assume a cash grant welfare program is instituted which pays M = 20 dollars for individuals who do not work. Compute the new optimal labour supply for this individual under the welfare program. Assume that prior to the welfare program, p =$1, w =$10, and V =$80 (as in part c). Does the individual accept the welfare program and not work? Show why or why not.

The utility of Amanda for leisure (L) and income (Y) is U = LY. The price of income is 1. If Amanda uses her spare L hours a day, (24 - L) hours will be labored. Since wages are w, the daily income is (24 - L). If the wages are positive, show that the optimal number of leisure hours that Amanda will use will always be the same. How much leisure time does Amanda demand and how much work time do she want to provide?

Consider a worker who consumes one good and has a preference for leisure. She maximizes the utility function u(x, L) = xL, where a represents consumption of the good and L represents leisure. Suppose that this worker can choose any L € [0, 1], and receives income w(1 – L); w represents the wage rate. Let p denote the price of the consumption good. In addition to her wage income, the worker also has a fixed income of y ≥ 0. (a) Write down the utility maximization problem for this consumer. Solution: The problem is max x L s.t. px ≤w(1 L) + y. x>0, LE [0,1] The budget constraint may also be written with equality since preferences are monotone. (b) Find the Marshallian demands for the consumption good and leisure. Solution: Using FOCs will find the maximum since preferences are Cobb-Douglas (and therefore convex). Dividing the FOCs L= Xp and x = Xw gives wL = px. Substituting into the budget constraint and checking the restriction L = [0, 1], we get and x(p, w, y) L(p, w, y) = = = 1 w+y…

21. Let U=x 2 +y 2 is the utility function of a worker who has 10 hours that to be allocatedbetween labour supply (L) and leisure (x). Let y is a consumption good whose price is 1.Wage rate (w) is Rs 1 and non-wage income is 20. Find out L.a) 10 b) 0 c) 5 d) 8 e) none 22. On the basis of the above question, hen w=0 and non-wage income is 40, find out L.a) 10 b) 0 c) 5 d) 8 e) none