11. A worker derives utility from consumption, C and leisure, L U = U(C, L) and initially faces the constraints p.C = N+w.H H = 24 - L where p is the nominal price of consumption, N> 0 is unearned income, w is the nominal wage and H is hours worked. (a) Derive the budget constraint in terms of C and L and show on a diagram an initial optimal choice of C and L, in which both are positive. (b) State this equilibrium algebraically, and briefly explain how it can be derived. (c) Show that, assuming normality of leisure, for some value N*, if N> N*, the individual will choose not to work. Is the initial level of N in your answers to parts a) and b) greater or less than N*?

11. A worker derives utility from consumption, C and leisure, L U = U(C, L) and initially faces the constraints p.C = N+w.H H = 24 - L where p is the nominal price of consumption, N> 0 is unearned income, w is the nominal wage and H is hours worked. (a) Derive the budget constraint in terms of C and L and show on a diagram an initial optimal choice of C and L, in which both are positive. (b) State this equilibrium algebraically, and briefly explain how it can be derived. (c) Show that, assuming normality of leisure, for some value N, if N> N, the individual will choose not to work. Is the initial level of N in your answers to parts a) and b) greater or less than N*?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter6: Demand Relationships Among Goods

Section: Chapter Questions

Problem 6.9P

See similar textbooks

Similar questions

Why does a change in income cause a parallel shift in the budget constraint?
For this question, assume that indifference curves are strictly convex, consumption andleisure are normal goods, and the optimal amounts of consumption, leisure, and labor arealways positive. A wage increase ______. (SE = substitution effect; IE = income effect)(a) increases labor supply via the SE and decreases labor supply via the IE(b) decreases labor supply via the SE and decreases labor supply via the IE(c) increases labor supply via the SE and increases labor supply via the IE(d) decreases labor supply via the SE and increases labor supply via the IE(e) Can’t tell without knowing the utility function
Problem Set 1. A firm's production function is º=50L-0.01Ľ' , where L denotes the size of the workforce. Find the value of MP in the case when: (a) L=1, (b) L=10, (c) L=100, (d) L=1000 Does the law of diminishing marginal productivity apply to this particular function? 2. Show that the price elasticity of demand is constant for demand functions of the form A P = Q" where A and n are positive constants. 3. The demand and total cost functions of a good are respectively 4P+Q-16=0 and ТС %3D 4 + 20 — 10 20 a) Find expressions for TR, (profit) 1 , MR, and MC in terms of Q. b) Solve the equation dn = 0 ÕP and hence determine the value of Q which maximizes profit. c) Verify that, at the point of maximum profit, MR=MC. 4. The cost of building an office complex, x floors high, in a prime location in Accra is made up of three components: (a) GH¢10 million for the land (b) GH¢'/, million per floor (e) Specialized costs of GH¢10000× per floor. How many floors should the office complex contain if…
Suppose a consumer has a monthly income of m = 100 which she spendson two commodities: french fries (x1) and beef jerky (x2). The price offrench fries is p1 = 2 and the price of beef jerky is p2 = 5.(a) Write down the consumer’s budget constraint (equation).(b) What is the maximal consumption of french fries (this is calledthe real income in french fries).(c) Find the maximal consumption of beef jerky (real income interms of beef jerky).
Suppose that a person has 2000 hours to allocate each year between leisure and work. a. Derive the equation of his budget constraint given an hourly wage of $(15)/hour. b) Graph his budget constraint line based on the equation you derived in part a. (Consumption (C) on the vertical axis and leisure (L) on the horizontal axis). Please make sure to include the value for the vertical and horizontal intercepts. c) Now suppose that the local government introduces an income guarantee program for single parents in which the income transfer is $10,000 per year if an individual does not work during that year (this dollar amount represents the benefit guarantee). If the individual decides to work, this transfer program imposes a 100% benefit reduction rate (e. g.. each additional hourly wage earned is reduced by 100%). Derive the new budget constraint equation that corresponds to this scenario. d) Draw the budget line that corresponds to the new scenario on a new graph. (Consumption (C) on the…
. An individual's utility function is given by u = 1000 x, + 450 x. + 5x, x. - 2x-x where x, is the amount of leisure measured in hours per week and x,is income earned measured in cedis per week. Det er mine the value of the marginal utilities, when x, = 138 and x= 500. Hence est imate the change in utility if the individual works for an extra hour, which increa ses earned income by GH¢ 15 per week. Does the law of diminishing ut ility hold for this function? %3D
1. An individual derives utility from the consumption of a basket of goods, c and leisure time, given by U(c, l) =cºl(1-a) where 0 < a < 1, is a constant; and must decide how to allocate her time between work, L and leisure to maximize her utility. The individual has a total of 24 hrs in a day (L + l = 24) and total consumption is constrained by her income; i.e., c = wL, where w the real per hour, is taken as given. (a) Solve for the optimal labor supply.
3. Draw and describe analytically the set of feasible consumption choices. What is the marginal rate of substitution at the optimal choice?
Question 1 Consider a person with the utility function U (C, L) = (1 − α) log C + α log L, where L is leisure time and C is consumption of other goods measured in dollars. The person has V dollars of non-labor income and a wage of w. There are T hours available for either working or leisure. 1. Write down the person’s budget constraint. Draw a graph representing this constraint, taking care to label the axes and key points. 2. What are the person’s marginal utilities for consumption and leisure? What is her marginal rate of substitution between leisure and consumption in terms of C, L, and α? 3. Write down a condition involving the person’s marginal rate of substitution that characterizes her optimal choice. Represent this condition graphically and interpret in words. 4. Solve for the person’s optimal choices of leisure and consumption, L ∗ and C ∗ , in terms of T, V , w, and α. 5. How does L ∗ change as you increase wage w and non-labor income V ? 6. How does C ∗ change as you…
4. Find the marginal rate of substitution in consumption for the utility function and determine its value at x = 2, y = 3 U (x, y) = 5x² + x²y + y2+6y
2. Suppose W-$15/hr. I income per week. N-hours of leisure per week. a. Find the equation of the income/leisure budget constraint. b. Graph the budget constraint. c. Find the weekly income of someone who chooses 15 hours of leisure per day. d. Suppose that by some miracle the number of hours in the day increased from 24 to 30 hours. Would this change the budget constraint? If your answer is yes, how would the budget constraint change. %3D
Juan is currently working in a job that pays $25 an hour and he chooses to work 8 hours per day. Assume that Juan can work a maximum of 16 hours a day, and he has complete flexibility in how many hours a day he works. Illustrate Juan’s budget constraint and his optimal choice of consumption and leisure. What is the slope of his budget constraint? What does this slope represent? (As on any graph you draw, make sure that you label the axes, the intercepts and the optimal choice.) Juan begins receiving a government transfer payment of $100 per day. Add his new budget constraint to your graph in (a) and show his new optimal choice. Does he choose more or less consumption? More or less leisure? Explain why for both goods. The government imposes a tax of 25% on Juan’s earnings from work and increases his government transfer to $150 per day (the government transfer payment is not taxed.) Redraw the budget constraint from part (b) (omit the part (a) budget constraint), and add a new budget…