Problem 1 Suppose a single parent has the following utility function: U-20 in C+10 In L....
Problem 5 Assume that a worker has the Utility Function U(C,L) C "C" refers to consumption in dollars and "L" to hours of leisure in a day. The worker has an offered wage of $10 per hour, 20 hours available for leisure or work per day, and $30 dollars a day from non- labour income. o 8.60 L (a) Find the budget constraint equation of the individual. (b) Find the optimal choice for the individual in terms of units of...
Suppose the representative household has the following utility function: U (C; l) = ln C + 0:5 ln l where C is consumption and l is leisure. The householdís time constraint is l+N=1 where Ns is the representative householdís labour supply. Further assume that the production function is Cobb-Douglas zK0:5 (N)0:5 where z = 1 and K = 1: 2.1 Assuming that the government spending is G = 0; use the Social Plannerís problem to solve for Pareto optimal numerical...
Suppose Tom has a utility function U=C*L C= consumption L= hours of leisure Tom has 100 hours to divide between work and leisure per week wage is $20/hr 1. Write down budget constraint in terms of consumption and hours of work 2.Tom make decisions on hours of work, leisure and consumption to max. utility. Explain why we can collapse this problem to one in which he chooses hours of leisure only 3. Find optimal hours of work and total consumption...
1. a. Naomi's utility function: U C is consumption L is leisure 75 x In(C)+300 x InL) Naomi's Budget Constraint is a little tricky Let's assume she is eligible for a government program that guarantees her S5000 a year for consumption and where the benefit is reduced by 50% for every dollar earned through working once she earns $10,000 she no longer receives the subsidy as it has been completely reduced by her income from working. If Sarah does decide...
John’s utility function is represented by the following: U(C,L) = (C-400)*(L-100), where C is expenditure on consumption goods and L is hours of leisure time. Suppose that John receives $150 per week in investment income regardless of how much he works. He earns a wage of $20 per hour. Assume that John has 110 non-sleeping hours a week that could be devoted to work. a. Graph John’s budget constraint. b. Find John’s optimal amount of consumption and leisure. c. John...
Let Tom's utility function be U(C, L) =C2+X×L2. Suppose he has 100 hours to split between work and leisure and he has no non-labor income. Derive Tom's optimal choice of consumption and leisure as a function of the wage and X. What is Tom's reservation wage?(Hint:Graphing an indierence curve before solving the problem might be useful.) *This is the correct utility function, copied directly from the homework.
Denise has utility over consumption c and leisure l defined by the following function: U(c, l) = c + l a) Suppose Denise has two units of consumption and three units of leisure. What is her utility? b) Suppose Denise has four units of consumption and one unit of leisure. What is her utility? c) Graph her indifference curves. Draw at least three separate indifference curves, for U = {2, 4, 6}. Label your axes accordingly.
Problem 1 Consider a consumer with the utility function U(21,22) = 10x 23 -50. Suppose the prices of X1 and 22 are 10 and 2 respectively and the consumer has an income of 150. How did the '50' in the utility function influence the optimal con- sumption bundle? How did the '10' in the utility function influence the optimal consumption bundle? (i.e., how would the optimal bun- dle change if these coefficients were to change?). How would the optimal bundle...
Question 1: Households A household's utility over consumption C and leisure l is U - U(C,0) Cl 1. Plot the household's indifference curve for U-80 for values of C andlless than 20 (i.e. find the curve containing all combinations of C and ( such that U(C, 0) 80) The household has a time endowment of h=16 hours per day. The wage rate per hour is w 1.25. The household's labour income is therefore wNs, where N-h-l-16- l is the time...
Suppose a consumer maximizes U(C,l)=ln(C)+ln(l), where C is consumption and l is leisure. The maximum time available for work and leisure is 1. Suppose a firm uses the following production function Y=z*Nd where Nd is labor used in production. The government collects a lump-sum tax T to finance government consumption G. Assume z=10 and G=6 and solve for the competitive equilibrium. What is the equilibrium wage rate? What is the equilibrium leisure level? What is the equilibrium consumption level? What...