1. -- ) and leisure ( L), U = CL². The wage rate is $20 per hour, the price of consumption is $10 per unit, and the consumer's non-labor income is $60. The time endowment of the consumer is 24 hours. I Consider a consumer who has the following utility function of consumption (C (1).( ) What's the utility-maximizing choice of consumption and leisure? (2).( Show that at that choice, the marginal rate of substitution between consumption and leisure is equal to the real wage.

1. -- ) and leisure ( L), U = CL². The wage rate is $20 per hour, the price of consumption is $10 per unit, and the consumer's non-labor income is $60. The time endowment of the consumer is 24 hours. I Consider a consumer who has the following utility function of consumption (C (1).( ) What's the utility-maximizing choice of consumption and leisure? (2).( Show that at that choice, the marginal rate of substitution between consumption and leisure is equal to the real wage.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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marginal utility is a measure of the benefit (or value, or enjoyment) a person obtains by a) Consuming a single additional unit of a product. b)Selling a single additional unit of a product (and spending the resulting cash). c) Borrowing the dollar value of a single additional unit of a product (and spending it on something nice). d)Converting a single additional unit of product to an equivalent number of units.
Please help me to solve questions (a) (b) (e). (especially question e). thank you!
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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*?
3. [30+10] A consumer who consumes two goods and has the following utility function: U(x₁, x₂) = log(x₁ + 1) + log(x2 + 1), where ₁ and ₂ denote the monthly consumption of two goods. The consumer maximizes her utility subject to the following constraints: P₁x1 + P₂x2 ≤m, x₁ ≥ 0, X₂ ≥ 0, where p₁ > 0, p2 > 0 and m > 0. [Hint: Note that log f(x) = f(df (2).] 1_df f(x) dx (a) Write down the Kuhn-Tucker conditions for a point (x₁, x2) to solve the problem, and find all points that satisfy the conditions. Do any of those points solve the problem? (b) Show the above results by drawing indifference curves and budget set on the x₁x2 plane.
5. Suppose the representative consumer has the (quasilinear) utility function: U(x, y) = ax + In(v) where x,y are consumption goods. Denominated in US dollars, the prices of x and y Pi and pz, respectively. (a) What does the term quasilinear mean? Is consumption of x independent of y? (b) Assume the consumer has a budget of C dollars at his/her disposal. What is the maximum utility the consumer may achieve with this budget? (c) What is the minimum expenditure if the consumer wants to derive U,units of utility?
1. Think about a utility function U(x,y) =xy, the budget constraint is px*x +py*y= m. m = 8, px=1, py=4. a. What is his optimal consumption? b. What is his maximum utility level? Now px has increased to 2. c. Based on expenditure function, after the price change, how much should be compensated to maintain his original utility level?
3. A consumer's indirect utility function is given by V (p, y) = f(p)y. (a) What is the form of this consumer's expenditure function? (b) What kind of preferences does this consumer have?
Terry attends college and works part-time in a drug store. She can work up to 40 hours each week and is paid $9 per hour. The following table shows her utility from different levels of leisure and income. Refer to the attached picture for the table. 1. Fill in the Marginal Utility columns above. 2. What will be Terry’s total utility from both leisure and income when working 20 hours per week?
2. Utility maximization - Trading off labor and leisure The indifference curves on the following graph show Amy's preferences for leisure and consumption for increasing levels of utility, such that her utility increases in both consumption and leisure. Assuming that Amy spends 68 hours each week sleeping, she has a maximum of 100 hours available to her for leisure if she does not work at all. Initially, she works 45 hours (and thus has 55 hours of leisure) and earns $250 per week. Use the grey point (star symbol) to indicate Amy's initial leisure/consumption bundle. Dashed drop lines will automatically extend to both axes. CONSUMPTION (Dollars per week) 1000 900 800 700 600 500 400 300 200 100 0 0 + 10 20 30 40 50 60 70 80 LEISURE (Hours per week) 90 U3 100 110 Initial bundle + $200 Unemployment Benefits Equivalent Bundle, $100 Unemployment Benefits Equivalent Bundle ?
part 3 4 5 Suppose Joan has a fixed income of 1000 and spends the entire income on commodity X and Y. The prices of commodity X and Y are 5 and 10 respectively.(i) Derive the consumer’s budget equation and sketch the line of this equation plotting Y on the vertical axis and X on the horizontal axis.(ii) What is the slope of the budget line (i) and what does it mean?(iii) Assuming income and price of X remain the same, show the effect of a 50 percent reduction in the price of Y on the consumer’s budget line.(iv) Show the effect of a 100 percent increase in income and a 50 percent reduction in prices on the consumer’s budget line.(v) If Joan’s U = X2Y2find the optimal bundle of X and Y that maximises Joan’s utility.
2. Suppose there are n identical consumers, each with a utility function u(x, y): = ax = x²+y. Each consumer has different disposable income w. The price of good x is p dollars, and the price of composite good y is equal to 1 dollar. Assume a > 0 and b > 0. (Hint: Question 1) (a) Calculate the marginal utility of good x and good y. Then, calculate the marginal rate of substitution between good x and good y. (b) Calculate the individual demand of consumer 1 for good x. (c) Calculate the aggregate demand for good x. (d) Draw a graph showing the market demand curve for good x. (e) Discuss whether an increase in disposable income for each consumer lead to an increase in the consumption of good x? This increase in disposable income can result from various factors, such as a decrease in taxes, government stipends, or other forms of income support. (f) Discuss the effect on demand for good x if there is an increase in the price of good x. This increase in the price of good x can result from…