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Labor Economics Problems

Problem 1: Income Leisure Model of Labor Economics

Problem 1. Income Leisure Model of Labour Economics Assume that a worker has the Utility Function U(C,L) = (C^2)(L) ; “C” refers to consumption in dollars and “L” to hours of leisure in a day. The worker has an offered wage of $”w” per hour, “T” hours available for leisure or work per day, and $”Yn” 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 leisure and income, the number of hours worked and utility obtained. c) Make a well labeled graph that illustrates the solution to the problem of the worker. d) Select your own values for T, Yn, w. You can select any values that make sense and are realistic. Find the solution to the problem that you created. You need to calculate the hours of work, the hours of leisure, the income, and the level of utility. e) What have you learn from doing or thinking about this problem? Problem 2 Labour Demand with Perfect Competition in the Labour Market and Perfect Competition in the Output Market in the Long Run. You are the manager of a business that operates in perfectly competitive markets {both the Labour Market and Output Market}. The production function of the business is given by: Q = 4(L^1/2)(K^1/4)  The price of the product is “100”. The wage rate is “W”. The price of capital is “1”. a) Find the use of labour and capital in the long run. You need to find L and K in terms of w. b) Explain the difference between the Short Run and Long Run.  c) Include a diagram for your solution. d) What have you learn from doing or thinking about this problem?
Problem 3 Labour Demand with Monopsony in the Labour Market and Monopoly in the Output Market in the Short Run. You are the manager of a business that operates as a Monopolist in the output market, and it is a Monopsonist in the local labour market. The production function of the business is given by: Q = 4L In the production function, Q is output, L is the number of workers employed, As a Monopolist, the firm faces a market demand given by: P = 100 - Q As a Monopsonist the firm faces a supply of labour given by the expression: w = 8L a) Calculate the equilibrium number of units of labour employed in short run. b) Briefly discuss the advantages for a firm of being a Monopolist in the output Market and a Monopsonist in the Labour Market and try to find a real life example of a firm that can modeled as a Monopolist/ Monopsonist. c) What have you learn from doing or thinking about this problem?Problem 4 Assume that there are two types of workers in a labour market with Utility Function given by:  Ux(w,s) = (w^2)s  and Uy(w,s) = ws^2 There is only one type of firms with isoprofit curve given by: π1(w,s) = (w^2 /, 200^2) + (s^2 / 100^2) – 1 = 0.   a) Calculate the optimal amount of wages and safety that the firm and the workers will negotiate. b) Make a detailed diagram of the solution. c) In simple words, briefly explain the theory of compensating wage differentials. d) What have you learn from doing or thinking about this problem?Problem 5A factory that you are managing has an hourly production process that can be represented by the following Cobb-Douglas production function: Q = (K^0.25)(L^0.25.) The price of one unit of capital per hour is $10 and the price of one unit of labour per hour is $20.  a) Find the optimal amount of labour and capital that you will be using to produce 100 units of output, b) Compute the total cost of producing 100 units of output. c) What have you learn from doing or thinking about this problem?

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