Everyone is endowed with 168 hours in a week (24X7). If you work 40 hours or les you w=$20 per hour. If you work overtime, you earn w=$25. Assume the worker ha M= non-labor income and that the price of the consumption good is p. Draw the budget constraint. Label the intercepts and the slopes in both the overtim
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- Consider an individual who receives utility from consumption, c, and leisure, l. The individual has L time to allocate to work, n, and leisure. The individual’s consumption is a function of how much he works. In particular, c = root n. The individual’s maximization problem is max U =ln(c)+θl subject to c = √n n+l=L where θ > 0. Solve the maximization problem. Hint: Substitute both constraints into the objective function.This question will analyze the impact on a person's labour supply from a shock to their partner's job. Assume leisure is a normal good. Let's assume Vanessa has a wage rate of $20 per hour. Recently her partner, Bill, had to take a wage cut at work, with his wage falling from $45 per hour to $30 per hour, but allowed them to continue working 40 hours per week. Analyze the decision of the household over choice consumption and Vanessa's leisure, taking Bill's hours as given (constant).The consumer's utility function for Consumption (C) and Leisure (L) is given as U(C,L) = √CLHis hourly wage is $10, non-labor income is $20; and he has a total of 16 hours to allocate between labor and leisureBased on this information, the consumer's total utility at the optimal level (or optimal C,L combination) is:a. 57.0 utilsb. 28.5 utilsc. 99.75 utilsd. 114.5 utilse. Cannot be determined with the information given I prefer typed answers.
- How would you demonstrate part b) diagramatically 6. Assume you can work as many hours you wish at £12 per hour (net of tax). If you do not work, you have no income. You have no ability to borrow or lend, so your consumption, c, is simply equal to your income. a) Derive and plot the feasible set, between daily values of consumption c, and “leisure”, l. Label the values at the intercepts (the points where the feasible frontier cuts the two axes). b) Assume that your optimal choice of consumption and leisure is to work 8 hours per day. Illustrate this choice diagrammatically using the feasible set and indifference curves.Assume you can work as many hours you wish at £12 per hour (net of tax). If you do not work, you have no income. You have no ability to borrow or lend, so your consumption, c, is simply equal to your income. Assume that your optimal choice of consumption and leisure is to work 8 hours per day. Illustrate this choice diagrammatically using the feasible set and indifference curves.Assume you can work as many hours you wish at £12 per hour (net of tax). If you do not work, you have no income. You have no ability to borrow or lend, so your consumption, c, is simply equal to your income. b) Assume that your optimal choice of consumption and leisure is to work 8 hours per day. Illustrate this choice diagrammatically using the feasible set and indifference curves.
- How would you demonstrate part c) diagramatically 6. Assume you can work as many hours you wish at £12 per hour (net of tax). If you do not work, you have no income. You have no ability to borrow or lend, so your consumption, c, is simply equal to your income. b) Assume that your optimal choice of consumption and leisure is to work 8 hours per day. Illustrate this choice diagrammatically using the feasible set and indifference curves. c) Use indifference curves and the feasible set to show why, given the properties of the optimal choice in part b), it is not optimal to work, say, 10, or 6 hours per day.Consider a representative agent with the utility function U = ln(Ct)+ Nt The budget constraint is Ct = wtNt +Dt where wt is the wage and Dt is non-wage income (i.e. a dividend from ownership in the firm). The agent lives for only one period (period t), and hence its problem is static. (a) Derive an optimality condition characterizing optimal household behav- ior. (b) Solve for the optimal quantities of consumption and labor. Plz do fast asap, urgent.Suppose that the owner of Boyer Construction is feeling the pinch of increased premiums associated with workers’ compensation and has decided to cut the wages of its two employees (Albert and Sid) from $23 per hour to $20 per hour. Assume that Albert and Sid view income and leisure as “goods,” that both experience a diminishing rate of marginal substitution between income and leisure, and that the workers have the same before- and after-tax budget constraints at each wage. Albert and Sid's opportunity set is presented below: "The horizontal axis labeled leisure hours ranges from 0 to 30 in increments of 5. The vertical axis is labeled income. A line begins at point A on the vertical axis goes down to the right and ends at the point (25, 0)." What is the value of A when the wage is $23? (Assume a 24-hour work day.) What is the value of A when the wage is $20? (Assume a 24-hour work day.) At the wage of $23 per hour, both Albert and Sid are observed to consume 13 hours of…
- Susan obtains utility by consuming carrots C and enjoying leisure L. Suppose that she has a daily non-wage income Y of £100 and is paid a fixed hourly wage rate of £10 for every hour she works in a local coffee shop. Assume that Susan is a utility maximiser and is free to choose x hours of work per day where 0 ≤ x ≤ 10. Assume also that the unit price of C is £1. a) Suppose that L is measured on the horizontal axis and C on the vertical axis. Use these axes to draw the set of all C and L combinations that Susan can choose from. Write down Susan’s budget equation. b) Suppose that Susan’s preferences over carrots and leisure are expressed by the following utility function: U(C,L) = min{C, 10L}. Calculate Susan’s optimal consumption bundle, both algebraically and graphically. Calculate the value of MRS at the optimal choice. c) Suppose instead that Susan’s preferences are such that indifference curves in the L-C space are strictly convex to the origin, and that she chooses to work 5…Q1: Suppose Labor and Capital are substitutes and the price of capital falls. All else equal, we should expect the labor select (supply, demand) Curve shift select ( up to the right, down to the left ) and for equilibrium wages to select (rise, fall) Q2: An individual has a utility function over Leisure and Income such that ?=?1/2?1/2 This individual has a budget constraint ?=?⋅(24−?)+? The best possible wage this individual can earn in the labor market is $2 per hour. This individual is $30 in debt (they have negative non-labor income). If this individual is earning a utility level of 4, which of the following are true? Group of answer choices The worker could be supplying 1 unit of Labor The worker could be earning $10 The worker could be supplying 8 units of labor The worker is maximizing their utility given their budget The worker's Marginal Rate of Substitution at the point where the budget constraint intersects the indifference curve is equal to -2Consider a couple (a husband and a wife) that jointly represents their collective preferences between combinations of household production time (X) and purchased goods and services (Y) according to the formula W = X2Y, where W represents the level of welfare. Suppose the maximum time available in a day is 16 hours and currently the wife devotes 6 hours to market work (H) at a wage of $16 per hour. a. What is the level of welfare associated with the wife’s current situation? b. How much additional purchasing power would the wife contribute if her market work hours increased to 8? c. How much of an increase in purchased goods and services would be necessary to compensate for the additional 2 hours of lost household production? d. Should this couple choose to have the wife increase her market work by 2 hours? e. If this couple is raising a child, suppose that combinations of household production and purchased goods are now ranked according to the formula U = X3Y. Would the additional 2…