Problem 1. (This is a very important problem)a) Create a new problem based on a topic that is of interest to you.b) Provide one possible answer to the problem. You must include mathematical equationsand graphs in your solution. You have to briefly explain your answer in your own words.c) Provide the reasons that made you create this problem.Problem 2.a) Name and explain in your own words the most important concept or theory or lessonthat you learned in this course? Why do you think so?b) What can/should you do with what you have learned from this course?c) Discuss and explain a concept or theory from the course that you found interesting.Please make sure to include diagrams and equations that might illustrate the theory.How would you apply this theory to explain something that you have observed?d) Discuss and explain a concept or theory from the course that you do not agree.Please make sure to include diagrams and equations that might illustrate the theory.e) Why you do not agree with this theory? Please provide reasons and justifications.Problem 3A consumer has set a budget of $100 for the consumption of good X and Y. The price ofGood X is $10, and the price of good Y is $20. The consumer has a Utility function given byU(X,Y) = xy 2 .a) Find the optimal consumption choice of the individual and the utility obtained.b) Make a graph that illustrates the solution to the problem.c) Briefly express in writing the process that you used to find the solution.d) Discuss some of the possible limitations of the Consumer Choice Model when it comes topredicting the behaviour of consumers.Problem 4Assume that a CONSUMER FACES Prices of $20 and $20 FOR GOOD X and GOOD Y, andthe consumer has a Utility function given by U(X,Y) = x 2/3 y. 1/3a) How much income (M) he/she should receive to obtain Utility of 200 units.b) Illustrate solution.c) Derive an equation for the demand for good X based on the Utility Function, the price ofY, and the income calculated.Problem 5a) Illustrate the typical earnings profile of Men and Women in most countries.b) Explain some of the reasons that we discussed in class that explain the different profiles.c) Provide one or two additional reasons from your observations of real life events.d) Suggest a policy that might help to reduce the earnings gap between men and women.e) Illustrate the typical earnings profile of Foreign born and local born individuals inCanada and the United States.f) Explain some of the reasons that we discussed in class that explain the different profiles.g) Provide one or two additional reasons from your observations of real life events.h) Do all groups of immigrants eventually obtain higher earnings than local individuals?Problem 6Labour Demand with Perfect Competition in the Labour Market and Perfect Competition inthe Output Market in the Long Run.You are the manager of a business that operates in perfectly competitive markets {both theLabour Market and Output Market}. The production function of the business is given by:Q = 2L 1/2 K 1/4 .The price of the product is “100”. The wage rate is “2”. The price of capital is “4”.a) Find the use of labour and capital in the long run.b) Explain the difference between the Short Run and Long Run.c) Include a diagram for your solution.Problem 7Assume that a worker has the Utility Function U(C,L) = CL“C” refers to consumption in dollars and “L” to hours of leisure in a day. The worker hasanoffered wage of $20 per hour, 20 hours available for leisure or work per day, and$100dollars a day from non-labour income.a) Calculate the amount of hours of work, hours of leisure and Consumption or Incomefor the worker.b) Briefly sketch a typical labour supply curvec) Calculate supply of labour equation.e) Calculate the reservation wage.Problem 8Labour Demand with Perfect Competition in the Labour Market and PerfectCompetition in the Output Market in Short Run.You are the manager of a business that operates in perfectly competitive markets {boththe Labour Market and Output Market}. The production function of the business isgiven by: Q = 10L 1/2 . The price of the product is 900. The wage rate is 40.a) Calculate the level of output and amount of labour hired by the firm.b) Derive the demand for labour (Hint: solve for L in terms of w).c) Calculate the elasticity of Labour Demand and interpret the result in WORDS.d) Make diagrams for your solutions.Problem 9Labour Demand with Monopsony in the Labour Market and Perfect Competition in theOutput Market in Short Run.Suppose a monopsony has a production function Q = 10,000L – 2L 2 The firm sells itsoutput in a perfectly competitive market at a price of $200 and its market supply oflabor is w = 30L.a) Determine the profit-maximizing level of employment and wage offered by the firm.b) Make a diagram. Explain why Marginal Cost of Labour increases at a faster rate thanthe wage rate.Problem 10a) Optimization of Labour inputs with Cost Constraint.A factory that you are managing has an hourly production process that can berepresented by the following Cobb Douglas Production function: Q = 40K 0.5 L 0.50The price of one unit of capital per hour is $30 and the price of one unit of labourper hour is $10. Your total cost should not exceed $1,000. Thus, TC = 2,000. Find theoptimal amount of labour and capital that you will be using, and compute the totalamount of Q. Include a diagram.b) Optimization of Labour inputs with Output Constraint.A factory that you are managing has an hourly production process that can berepresented by the following Cobb Douglas Production function: Q = 40K 0.5 L 0.5 Theprice of one unit of capital per hour is $20 and the price of one unit of labour perhour is $20. You have been to produce 20 units per hour or Q = 30. Find the optimalamount of labour and capital that you will be using, and compute the total cost.
