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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.Production Analysis Q. I The economist for the ABC Truck Manufacturing Corporation has calculated a production function for the manufacture of their medium-size trucks as follows: Q =13 1PKG where O is number of trucks produced per week. & is number of labor hours per day, and & is the daily usage of capital investment. a. Does the equation exhibit increasing, constant, or decreasing returns to scale? Why? b. How many trucks will be produced per week with the following amounts of labor and capital? Labor Capital 100 50 120 50 150 75 200 100 300 150 c. If capital and labor both are increased by 10 percent. what will be the percentage increase in quantity produced? d. Assume only labor increases by 10 percent. What will be the percentage increase in production? What does this result imply about marginal product of labor? e. Assume only capital increases by 10 percent. What will be the percentage increase in production? f. How would your answers change if the production function were -1.3 [WA " instead? What are the implications of this production function? Show in graph. Q. 2 Show in a diagram what changes will occur as a result of the changes listed. a. The firm's budget increases. b. The price of Y decreases. c. The price of X decreases. d. Y becomes more expensive, and X becomes less expensive. e. Technology makes the Y input more productive. f. Technology increases the productivity of both inputs by the same proportion. Q.3 The owner of a car wash is trying to decide on the number of people to employ based on the following short-run production function: Q= 66 - 0.56- where Q is Number of car washes per hour, L is Number of workers a, Generate a schedule showing total product, average product, and marginal product. b. Suppose the price of a basic car wash in his area of business is $5. How many people should he hire if he pays each worker $6/hour? c. Suppose he considers hiring students on a part-time basis for S/hour. Do you think he should hire more workers at this lower rate? Explain, Q.4 In a wheat market: Qd = 3550 -266P and Q3 - 1800 + 240 P I, Find the equilibrium for this market both numerically and graphically. Il. Find the point price elasticity of demand and the point-price elasticity of supply at the equilibrium price. Are the producers going to gain in terms of their total revenue if there is an increase in price? Explain. Ill. Following a severe drought the regulators in this market wish to boost production in this market. They decide to implement a price floor by choosing a price higher the equilibrium market price. Explain the impact of such a policy on the quantity of wheat that will be bought and sold in the market and its impact on efficiency. Is this going to create a gap between demand and supply? Explain using an appropriate graph. IV. Do you think that the Indian Policy makers have ever used such a price-policy?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)e) (12 points) Graph these curves: a. profit-maximizing labor demand: part d (w on vertical axis, L on horizontal axis) b. short-run supply: part b (P on vertical axis, q on horizontal axis) c. profit: from above (T on vertical axis cal axis, P on horizontal axis) The graphs do not need to be super-accurate but pay attention to the shape of the curves and where they intersect the axes (if they do) () (12 points) Suppose P = P. On the 3 graphs from part e, show what happens when w increases from w, to Wa. Explain how and why labor, supply, and profit change. 2. (54 points) Short-run costs. Suppose w = 1, r = 10 and K = 20. a) (5 points) We have TC = w (#) q' + rk = ()q'+ 200 On one graph (with q on the horizontal axis), graph the Total Cost, Variable Cost, and Fixed Cost functions. Pay attention to the shape of the curves, where they intercept the axes and each other (if they do), and the position of the curves relative to each other. b) (9 points) Using the graph from part a. show how AC, AVC, and MC can be shown when q = 20. c) (5 points) From the TC function in part a, find Marginal Cost, Average Cost, and Average Variable Cost. d) (8 points) Use the function you found in part c. On one graph (with q on the horizontal axis), graph the AC, AVC, and MC functions. Pay attention to the shape of the curves, where they intercept the axes and each other (if they do), and the position of the curves relative to each other. e) (6 points) Calculate the values of AC, AVC, and MC when q = 20. Show these points on the graph from part d. Relative to each other, are the values for AC, AVC, and MC at q = 20 consistent with the results in part b? () (6 points) Calculate the price at which this firm would break even (zero profit). What is the optimal output at this price? 9) (15 points) Suppose the market price is P = 20, What is the firm's optimal output and profit? With respect to profitability, what is the firm's optimal course of action? Explain