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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, 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 w2- 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 (*) q3 + rk = ()q3 + 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? f) (6 points) Calculate the price at which this firm would break even (zero profit). What is the optimal output at this price? g) (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.Consider a price-taking firm with this production function: q = 1 1/3 K1/3 1. (46 points) Operating in the short-run. a) (4 points) Show that the total cost function is TC = w ()q3 + rk b) (6 points) Show that the short-run supply function is q = ( (PK) 1/2 c) (6 points) What is the short-run supply function? Why? d) (6 points) Show that the profit-maximizing labor demand function is L = K1/2 () 3/2 The profit function is * = (3) p4/3 ( K ) 1/3 -rk I = TR - TC = Pq - (wl trk) = p(PK) 1/2 - WK1/2 ( _) 3/2 - rk = P3/2 ( K )1 3/2 3w - Wk1/2p3/2 (4)"(1) *- TK = P3/2 ( K 3w/ *- p3/2 ()"()()" - rK = p3/2 ( K 1/2 - P3/2 ( K \\1/2 (3w/ -rk = p3/2 (K (3 w/ (1 -1) -TK = (2) P3/2 (4)1/2 3 w -rkSuppose you are estimating parameters of the following regression model: Y = B, + B2X2 + ByXx + Le Where: Y, = average starting pay at graduation, in pounds. Xx = tuition fee in 2012, in pounds. X = independent recruiter rating (maximum is 5.0). ur = disturbance term. Using cross-section data on top 50 UK graduate business schools, you obtain the following results: Y, = 9941 + 0.25 X2t + 15125 X3t (6114) (0.121) (7349) R' = 0.87, RSS = 10310 (The figures in parentheses are the estimated standard errors. RSS are residual sum of squares.) (i) Comment on the signs of the variables in the model. (2 Marks) (ii) Interpret and explain individual coefficients. (4 Marks) (iii) Suppose X3 increases by 0.25; what is the expected impact of this change on Y? (2 Marks) (iv) Comment on the explanatory power of the regression. (2 Marks) (v) Using t-tests show whether individual coefficients are significantly different from zero at 5% level of significance. (4 Marks) (vi) Test whether the coefficient of X, is significantly different from 1 at 5% level of significance. (2 Marks) (vii) Carry out an appropriate test to check if coefficients are jointly significant. (5 Marks)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 = 1.3 1035 Kal where O is number of trucks produced per week, L is number of labor hours per day, and K 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 60 150 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 10 7 0 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. c. 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: 0= 61 - 0.513 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 $4/hour. Do you think he should hire more workers at this lower rate? Explain. 9.4 In a wheat market: Qd = 3550-266P and Qs = 1800 + 240 P 1. 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