Answer with clear explanation.

Question 1 (total 15 points). A firm has a production function:f (K, Z) = 50LK05 + L2 K2 - 13 K3 a. What is its short-run production function if capital is fixed at K=4? b. What are the firm's marginal product of labour and average product of labour in the short run? c. Calculate the elasticity of output with respect to labour. Question 2 (total 16 points) . Do the following functions exhibit increasing, constant, or decreasing returns to scale? Explain your answers. a. The production function ( = 17054054.", where A is materials, K is capital and L is labour. b. q = L +0.5K c. q = 0.5LK0.25 d. q=413 +4K Question 3 (12 points). Find the Marginal Rate of Technical Substitution for the following production functions: a. q= Liki b. q=L0.5 + K0.5 C. q -L +K Question 4 (Total 10 points). Suppose a firm's cost function is C =2q - 16q' + 90q, average cost curve is described by the equation AC = 2q- - 16q +90. At what output level does the marginal cost curve cross the average cost curve? Question 5. (16 points, 8 points each) For the following, please answer "True" or "False" and explain why. a. When buying a piece of equipment, it is always best for the firm to pay cash instead of borrowing the funds since this renders the equipment less costly. b. University of Toronto is choosing a location for a new building. The university has campuses at Downtown, Scarborough and Mississauga. A large parcel of land would have to be purchased at Scarborough or Mississauga if the building were to -Page 1- be built there. So it is cost-effective to locate the new building at downtown because the university already owns the land.1- The data collected for USA over the period of 1950-2010. The following equation is estimated log(D.)=-2.88+1.06log(Y.) (0.12) (0.293) where D, is defense expenditure and Y is GDP. Standard errors are in parenthesis. Find 95% confidence interval for parameters and interpret the parameter estimates. 2-We aim to fit following model EARNINGS = B, + B.SM + B,SF + B,Math +u where hourly EARNINGS is regressed on a constant, Schooling of Mother (SM), Schooling of Father (SF) and Mathematical Capability (Math). Hourly earnings are measured in dollar, SM and SF are measured in schooling year and Math is measured by exam results. Regression analysis produces following output Dependent Variable: EARNINGS Method: Least Squares Sample: 540 Included observations: 540 Variable Coefficient Std. Error t-Statistic Prob. C -14.65851 3.589279 -4.083972 0.0001 SF 0.668173 0.220817 3.025912 0.0026 SM 0.277970 0.290546 0.956715 0.3391 Math 0.458015 0.066418 6.895906 0.0000 R-squared 0.166245 Mean dependent var 19.71924 Adjusted R-squared 0.161579 S.D. dependent var 14.60151 a-Interpret the parameter estimates (considering the test statistics). b- Comment on the goodness of fit of the model. C- A researcher claims that educated man/women prefer to get married to educated women/men. Suppose this argument is empirically verified for those individuals. Reassess the estimation results in the light of this evidence. d- It is claimed that the total effects of SM and SF on earnings is 1. Explain how you can this claim. Give all the details. d- A researcher calculates parent education as SP=SM+SF. Explain what would happen if the following model is estimated. EARNINGS = 6, + B,SM + B,SF + B,Math + +B,SP+u (2)TOSUIT IS TOU THOCITOI WY IIQUE PIVUUGAIN 11. How can the externality be addressed. Name 3 ways. And explain. 12. Draw a graph of a good with a positive externality and explain whether the result is too much or not enough production. 13. How can the externality be addressed. Name two ways and explain. 14. There are some solutions that are theoretically possible but not realistic for solving externalities. Why do they fail in practice? 15. Explain what a specific example of a public good is and who takes advantage(abuses/defrauds) of them, how/why? 16. Explain what a specific common resource is and who takes advantage(abuses/defrauds) of them, how/why? 17. What could be done to correct question 15? 18. What could be done to correct question 16? 19, Economics may be a study of scarcity, but it is also a study of equity as well. Would you be happy with the solutions you put forward in questions 17 & 18? Why or why not? 20. Who pays their fair share of taxes?(this is a trick question) explain 21. Who pays their unfair share of taxes?(this is also a trick question)explain 22. Explain how at least three different types of taxes discriminate against some groups and are fair or unfair as we have chosen to implement them in the United States. 23. Why have we chosen to set taxes up this way do you think? 24. What are implicit and explicit costs? 25. Why does the production function's slope decrease? 26. Why does the average fixed cost curve decrease as output increases? 27. When do firms decide to shut down in the short or long term? Why is their decision different? 28. Why are Monopolies a concern for society? What can they do that would lead to a sub- optimal outcome? 29. What has been done to remedy a monopoly and do you think there are any monopolies today that need to be addressed?1. Assume that the market for steel is competitive. The inverse demand curve for steel is P = 120 - Q and its inverse supply (i.e., industry marginal cost) curve is P = Q + 20, where P is price and Q is quantity. (a) Depict these inverse demand and supply curves in a diagram and use algebra to calculate the market equilibrium values of price, Pe, quantity, Qc, and price elasticity of demand, Ec. [10 points] (b) In the above context, also calculate consumer surplus, CS, producer surplus, PS, and social welfare, SWc. [10 points] 2. Suppose that the industry in Question I is taken over by a monopolist. (a) Depict the monopolist's profit maximization problem in a diagram and use algebra to solve for the values of price, Pm, quantity Om, and price elasticity of demand, Em. [10 points] (b) Calculate the impacts of monopolization in terms of the resulting changes in consumer surplus, producer surplus, and social welfare. [10 points] 3. (a) Return to the scenario in Question 1 and assume that the process of producing steel causes air and water pollution, which result in marginal external cost MEC = 20. Taking this externality into consideration, calculate the socially optimal level of steel production, Q, and illustrate its determination in a diagram like the one for Question 1(a) by using any additional curve that may be needed. Also calculate social welfare, SWs. [10 points] (b) If the competitive market fails to account for external costs and continues to produce at Q (from Question 1(a)), what would be the resulting loss in social welfare? Explain your calculation with the help of a diagram. [5 points] (c) Calculate a per unit tax that could correct the market failure in part (b). If this tax is implemented, what would be the resulting values of social welfare, consumer surplus, producer surplus, total external costs, and total tax revenue? Also illustrate these areas in a diagram. [15 points]