. Explain the following attachments

1. What does a positive linear relationship between x and y in a simple regression imply? (a) Increases in the independent variable are usually accompanied by increases in the regressor (b) The relationship between x and y cannot be explained by a straight line (c) Decreases in the independent variable is usually accompanied by increases in the regressors (d) Increases in the regressor are usually accompanied by increases in the dependent variable.1) Consider the following short-run production function: Q = 5L" ll? 3 where Q is the output and Lie amount oflabor. (a) Calculate average product of labor. (b) Calculate marginal product of labor. (c) Calculate level of L at which labor productivity is maximized. (d) At what level of L do diminishing marginal returns begin? (e) Calculate the range of Lin region I of production (region of increasing marginal returns). (t) Calculate the range of Lin region I] of production (region of decreasing marginal returns). I. A nn's production function is given by is q = KL 0.8K2 0.2!,2 where q is the quantity of output produced, I. is the amount of labor input used, and K is the amount of capital input used. Suppose the amount of capital is fixed at 10 units of capital in the short run. I. 2. Find this finn's short run (a) total product of labor function, (b) average product of labor function, and (c) marginal product of labor function. At what level of labor input usage does the marginal productivity of labor reach a maximum? How much output is produced at that point? Show and briey discuss how you arrived at your answer. Is the marginal product of labor ever negative for this production function? If so, when. If not why not. Show how you arrived at your answer. At what level of labor input usage does the average productivity of labor reach a maximum? How much output is pmduced at that point? Show and briey discuss how you arrived at your answer. At what level of labor input usage does the total productivity of labor reach a. maximum? How much output is produced at that point? Show and briey discuss how you arrived at your answer. What is the economic region of the short run production function you found in part I? Show and briey explain how you arrived at your answer. Calculate the output elasticity of labor when this rm uses the amount of labor at which its average product of labor is maximum. In a carefully labeled diagram, graphically illustrate this rm's total product of labor in the upper panel and the marginal product of labor and average product of labor in the lower panel using your results in parts 1 to 4. Suppose you are estimating parameters of the following regression model: Y = By + B2X2 + By Xx + 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). It = 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)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