Question

In: Economics

Suppose Joe has utility U = min(C/60, L) i.e. Joe must have $60 and an hour...

Suppose Joe has utility U = min(C/60, L) i.e. Joe must have $60 and an hour of leisure to get one util.. By extension $30 and 30 minutes of leisure gives him 0.5 utils and $120 and 2 hours of leisure gives him 2 utils. Further, assume that Joe can make $20/hour at his job and has absolutely no savings. Lastly… assume Joe must sleep 8 hours a day (which counts as neither work nor leisure), but can work and/or leisure up to the remaining 16 hours (with fractional hours of work / leisure allowed as well). Joe is trying to figure out how to spend his day.

  1. Draw Joe’s budget set i.e. draw all combinations of consumption and Leisure Joe can afford.
  2. On a separate graph 2 indifference curves: one showing all points where Joe has 2 utils and another where Joe has 4 utils.
  3. What is Joe’s optimal consumption of Labor and Leisure on this day?

Solutions

Expert Solution

(a) The budget constraint would be , for N be the labor hours, and hence N+L=16, and hence, the budget would be or or . The graph is as below (note that the graph is scaled to look clean).

(b) The two indifference curve would have the equation and .

(c) The corner of the indifference would be at where , which would be the utility maximizing combination, irrespective of price of C and L. Putting it in the budget constraint, we have or or or , and since , we have . These are the utility maximizing combination of affordable C and L. The graph is as below.

Rahul Sunny answered 2 years ago
Next > < Previous

Related Solutions

Suppose that the utility function is U(c, l) = c^(a) l^(1−a) where < a < 1....
Suppose that the utility function is U(c, l) = c^(a) l^(1−a) where < a < 1. Calculate the slope of an indifference curve for this utility function. What happens to the slope of the indifference curve when c decreases and l increases? Explain.
Shelly’s preferences for consumption and leisure can be expressed as U(C, L) = min(C,2L) This utility...
Shelly’s preferences for consumption and leisure can be expressed as U(C, L) = min(C,2L) This utility function implies that Shelly views consumption and leisure as compliments. There are 110 (non-sleeping) hours in the week available to split between work and leisure. Shelly earns $10 per hour after taxes. She also receives $320 worth of welfare benefits each week regardless of how much she works. a) Graph Shelly’s budget line. b) Find Shelly’s optimal amount of consumption and leisure. c) What...
Say the household has utility U (c, l) = c + log (l) and is endowed...
Say the household has utility U (c, l) = c + log (l) and is endowed with h = 1 units of time and no units of capital. The government has planned expenditures of G = 1. The firm's production technology is Y = 4N. Now assume that the government cannot finance G trough a lump-sum tax, but has to rely on a proportional tax on income. Solve for the value (or values) of τ that allows the government to...
Suppose that a representative consumer has the following utility function: U(C,L)=5ln(C)+2ln(L) and she has the budget...
Suppose that a representative consumer has the following utility function: U(C,L)=5ln(C)+2ln(L) and she has the budget constraint w(h-L)+pie-T. Derive the consumer's rules for consumption and leisure (solve for consumption and leisure "demand functions" as a function of exogenous variables). Graph and discuss the income and substitution effects for a consumer if her wages decreased (with labels).
Assume that a worker has the Utility Function U(C,L) = C 0.25​ ​ L0.75​ “C” refers...
Assume that a worker has the Utility Function U(C,L) = C 0.25​ ​ L0.75​ “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 $90 dollars a day from non-labour income. a)     ​ Find the budget constraint equation of the individual.​                   b)    ​ Find the optimal choice for the individual in terms of units of...
Robert has utility function u(c,l) = cl over consumption, c, and leisure, l. Robert is endowed...
Robert has utility function u(c,l) = cl over consumption, c, and leisure, l. Robert is endowed with 16 hours of leisure. Let the price of consumption be p = 1. Robert can sell his time in the labor market at hourly wage, w. The equilibrium we will consider implies zero firm profits, so labor income is the only source of income for consumers. Thus, Robert’s budget line can be written by c + wl = 16w. Production of the consumption...
Robert has utility function u(c,l) = cl over consumption, c, and leisure, l. Robert is endowed...
Robert has utility function u(c,l) = cl over consumption, c, and leisure, l. Robert is endowed with 16 hours of leisure. Let the price of consumption be p = 1. Robert can sell his time in the labor market at hourly wage, w. The equilibrium we will consider implies zero firm profits, so labor income is the only source of income for consumers. Thus, Robert’s budget line can be written by c + wl = 16w. Production of the consumption...
Suppose a worker's utility function is U(C, L) = C^2 +(2nL)^2 , where C denotes consumption...
Suppose a worker's utility function is U(C, L) = C^2 +(2nL)^2 , where C denotes consumption and L leisure. Let T denote time available to split between leisure and work, w denote the wage rate and V = 0 denote non-labor income (as in the lecture). (a) What is the worker's optimal choice of C and L as a function of w, T, and n? (b) What is the worker's reservation wage as a function of T and n? (c)...
Consider an individual with the following utility function: U = min{c, h} Where c is consumption...
Consider an individual with the following utility function: U = min{c, h} Where c is consumption and h is leisure. The wage rate is $15 per hour, and the total number of hours available to the individual is normalized to 1. Find out the optimal level of consumption, leisure and labor. The government imposes a tax of $2 per hour of labor. Find out the new optimal values of consumption, leisure and labor. Comment on the form of the utility...
8、Assume that utility depends on consumption c and leisure l , U(c,l) . (a) Define reservation...
8、Assume that utility depends on consumption c and leisure l , U(c,l) . (a) Define reservation wage. (b) “The reservation wage increases with (i) non-labor income, (ii) fixed monetary costs of work, (iii) fixed time costs of work, and (iv) the price of consumption.” Prove or disprove each of these four claims.
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT