Consider the utility function u (c, o) = oc (o = leisure; c = consumption), determine the optimal amount of consumption and leisure if the consumer can work at most 24 hours, the hourly wage is 5 and the price of each unit of consumption is 2. There is no initial income endowment.
Consider the utility function u (c, o) = oc (o = leisure; c = consumption), determine...
Problem 3 Alan's utility function for consumption (C) and leisure time (1) is U(C,1) = 2C1/2 + 1. Each week, Alan has a time endowment of 120 hours that he can devote to work (N) or leisure time (7). The unit price of C is $1 while the unit wage rate is w. Alan also earns A dollars per week of non-labor income. a) Write the expression of Alan's budget constraint. b) Find Alan's optimal combination of consumption and leisure...
Problem 3 Alan's utility function for consumption (C) and leisure time (1) is U(C,1) = 2C1/2 + 1. Each week, Alan has a time endowment of 120 hours that he can devote to work (N) or leisure time (7). The unit price of C is $1 while the unit wage rate is w. Alan also earns A dollars per week of non-labor income. a) Write the expression of Alan's budget constraint. b) Find Alan's optimal combination of consumption and leisure...
Clark gains utility from consumption c and leisure l and his preferences for consumption and leisure can be expressed as U(c, l) = 2(√ c)(l). This utility function implies that Clark’s marginal utility of leisure is 2√ c and his marginal utility of consumption is l √ c . He has 16 hours per day to allocate between leisure (l) and work (h). His hourly wage is $12 after taxes. Clark also receives a daily check of $30 from the...
Consider a consumer who derives utility from two goods: consumption (Good C) and leisure (Good H, in hours). The consumer has a total of L hours available. The consumer's income comes from time spent at work, which pays a wage of w per hour. Assume the three activities are mutually exclusive: While at work, the consumer cannot spend time on leisure or consumption. (a) What is the consumer's budget constraint? (b) Assuming the consumer's utility function is U(c,h)=a*ln(c)+(1-a)ln(h), derive the...
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...
4. Let a person's utility function over consumption, X, and leisure, L, be given by U = XL2, SO MUx = L2 and MUL = 2xL.The individual may work up to 24 hours per day at wage rate, w = $10 per hour, and he has non-labor income of $50 per day. The price of x, px, is $5. (a) Find the utility-maximizing x and L. (b) Show that at the utility- maximizing quantities of x and L, the consumer's...
13) Consider the standard labor-leisure choice model. Consumer gets utility from consumption (C) and leisure (L). She has H total hours. She works N S hours and receives the hourly wage, w. She has some non-labor income π and pays lump-sum tax T. Further suppose (π – T) > 0. The shape of utility function is downward-sloping and bowed-in towards the origin (the standard U- shaped case just like a cobb-douglas function) If this consumer decides to NOT WORK AT...
4. Consider the consumption-leisure choice model we discussed in class. Suppose individual utility is represented by the function U(c, L) = min {c, 10L}, where c is consumption and L is leisure. Individuals have a total h = 16 hours that could be divided into work and leisure. Market wage rate is w = 10. (a) Sketch the individual’s indifference curve. (b) Find the optimal consumption and leisure choice. (c) Now suppose wage increases to w = 12. Find the...
Consider a representative consumer who has preferences over an aggregate consumption good c and leisure l. Her preferences are described by the utility function: U(c,l) = ln(c) + ln(l) The consumer has a time endowment of h hours which can be used to work at the market or enjoyed as leisure. The real wage rate is w per hour. The worker pays a proportional wage tax of rate t, so the worker’s after-tax wage is (1−t)w. The consumer also has...
intermediate micro
4. Steve's utility function over leisure and consumption is given by NLY) - min (31.7. Wage rate is w and the price of the composite consumption good is p=1. (a) Suppose w = 5. Find the optimal leisure consumption combination. What is the amount of hours worked? (b) Suppose the overtime law is passed so that every worker needs to be paid 1.5 times their current wage for hours worked beyond the first 8 hours, Will this law...