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##### Economics 304-The production technology of a firm is given in the table below

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Question;1. (55 points total ? 5 points for each of 7 parts - a. through g., 10 points for part h. and the diagram plus 10 for diagram)The production technology of a firm is given in the table below.Number of workersUnits of outputMPN0014828831184144516661847196a. Define the marginal product of labor,, explain how it relates to the production function (with N on horizontal axis and Y on vertical axis) and find the marginal product of labor (MPN) for each level of employment (fill in the third column of table).b. Assume that the price of a unit of output is $10. Calculate the number of workers that will be hired if the nominal wage rate = $290. Calculate the number of workers the firm will hire if the nominal wage is $250. Calculate the number of workers that the firm will hire if the nominal wage is $200.Draw a production function and real labor demand curve vertically with the PF on top (like we do in class), labeling point A as the wage / price combo of $290 / $10, point B as the $250 / $10 combo, and point C as the $200 / $10 wage / price combo. Be sure to label your diagram completely.A correct and completely labeled diagram is worth 10 pointsc. What could cause wages to fall like this (name and support 2 reasons)?d. Why exactly does the firm?s behavior change when the nominal wage changes, all else constant? Make sure you refer to the profit maximizing condition when answering this question. Please discuss in real terms, not nominal terms.e. Let?s return back to the initial conditions in the beginning of part b, with prices at $10 and nominal wages at $290 (point A). Now we let prices change and fall from $10 to $8, holding nominal wages constant at $290. What could cause such a price change (name at least 2 reasons)? Hint, think of economics 102.f. Locate this ?new? point as point D on your two diagrams. Similar to part d) why exactly does the firm?s behavior change when prices fall from $10 to $8, all else constant? Again, make sure you refer to the profit maximizing condition when answering this question. Please discuss in real terms, not nominal terms.g. Let?s return to point A, the initial conditions where the nominal wage rate = $290 and the price of a unit of output = $10. Assume that a new technology increases the number of units of output that each worker can produce by 10 units of output (i.e., each worker's MPN rises by 10). Calculate the number of workers that the firm will hire and the number of units of output that will be produced (fill in the table below).Number of workersUnits of outputMPN001234567Now locate this point as point E on both diagrams. Again, make sure you label diagram completely or points will be taken off.h. (10 points) Comment on the macroeconomic implications of this technology shock (as in assume many firms in the economy experience similar technology shocks) on prices (inflation), employment and the unemployment rate, economic growth, pressure on real wages, the stock market via the profit implications, and the budgetary implications for the Federal Government (make sure you refer to each economic variable).2. (50 points total ? 5 for each of 8 parts and 10 for diagram)This current event is no longer current but it still works!January 28, 2014, 10:47 AM ETObama to Raise Minimum Wage for Federal Contractors, Asserting Executive PowerPresident Barack Obama plans to act unilaterally to raise the minimum wage for employees of federal contractors, a move that asserts his executive powers before his State of the Union address in which he will press Congress to approve a broader increase this year, write Carol E. Lee and Eric Morath. Read the full WSJ story here.The executive order would raise the minimum wage for workers on new federal contracts to $10.10 an hour, according to a fact sheet from a White House official. It said Mr. Obama would announce the new policy in his speech Tuesday, which is scheduled to begin at 9 p.m. Eastern Time.The federal minimum wage is $7.25 per hour, and hasn?t been raised since July 2009. About 22,000 federal employees were paid at or below minimum wage in 2012, according to the Labor Department. The agency doesn?t specify how many employees were government contractors.Suppose the marginal productivity of labor for a federal employee is given by:MPN = 51 - 2N.The labor supply curve for federal employees is estimated to be:NS = 15 + wN is denominated in thousands of workers2a) Compute equilibrium values for the real wage and employment.Illustrate this equilibrium on a labor market diagram in real wage space. Please be sure you label the diagram completely (with all the shift variable included) and label this initial equilibrium point as point A.A correct and completely labeled diagram is worth 10 points2b) Now the executive order from President Obama - he is forcing (mandating) the real wage to be 10 (actually it is the nominal wage at $10.10 but let's pretend it is the real wage at 10). What is the level of employment now?2c) Compare the number of people willing to work vs. the number of people that are hired. What do we call the difference in these values when the quantity of labor supplied exceeds the quantity of labor demanded? Add these two points to your diagram and label these points as point(s) B. Make sure you identify the unemployed in your diagram.2d) The intuition part 1: Why exactly did we move along the labor demand curve? In particular, why does the profit maximizing level of labor input change with the minimum wage program (make sure you write out the profit maximizing condition and explain why it has changed i.e., why do employers rationally change their quantity demanded of labor the way they did)? Be very specific with numbers (i.e., use numbers in your explanation).2e) The intuition part 2. We also experience a movement along the labor supply curve. Explain the intuition here as in why are more people are willing to work using and explaining the substitution and income effects associated with labor supply. Which effect dominates and what has happened to the price of leisure for those that are still working, given the executive order?2f) Suppose now that instead of raising the minimum wage, the federal government offers a training program to these same federal employees so that their human capital rises. As a result, the new marginal product of labor is now:MPN = 60 ? 2N.Find the equilibrium ?market? clearing wage and level of employment. Please show all work below.Please depict this new development on your original diagram labeling this new equilibrium point as point C. Be sure to label diagram completely.2g) Compare the welfare of the workers under the two scenarios: 1) the minimum wage program vs. 2) no minimum wage program but with the training program. In other words, are workers better off in part b) or are they better off in part f)? Be sure to explain.2h) Compare the welfare of the firm, the employer. Is the firm better off in terms of profits in part b) or in part f)? Be sure to explain (feel free to refer to the plastering example and/or the new economy).3. (55 points total ? 5 for each of eight parts and 15 points for diagram)An economy?s aggregate production function is given by Y = A?K?N ? N2. The marginal product of labor for this production function is MPN = A?K ? 2N.(a) Assume that A = 10 and K = 10. Suppose that the labor supply function for this economy is given by NS = 10 + 2w. Find the equilibrium real wage rate, the full employment level of employment, and the full-employment level of output for this economy.Draw a production function and labor market diagram vertically as we did in class (many times) and label this initial equilibrium point as point A.A correct and completely labeled diagram is worth 15 points (remember to put shift variables in parentheses next to the relevant functions).(b) Suppose that a new innovation leads to an increase in total factor productivity so that A increases to 12. Everything else remains as in part (a). Find the equilibrium real wage rate, the full employment level of employment, and the full-employment level of output for this economy and label on your diagrams as point B.(c) Explain exactly why the profit maximizing level of labor has changed given the increase in total factor productivity. Again be very specific with your answer as in using numbers. Begin your answer with: At the same level of labor input N* = (what it was at point A), the firm is no longer.............(d) Let?s go back to our initial conditions (point A). Instead of a new innovation impacting the economy, assume that severe weather destroys a portion of the capital stock, so that K = 8. Everything else is as it was in part (a). (In particular, A = 10.) Find the new levels of the equilibrium real wage rate, the full employment level of employment, and the full-employment level of output for this economy and label (on both diagrams) as point C.(e) (c) Explain exactly why the profit maximizing level of labor has changed given the adverse shock to the capital stock (K). Again be very specific with your answer as in using numbers. Begin your answer with: At the same level of labor input N* = (what it was at point A), the firm is no longer.............(f) Instead of a new innovation or bad weather impacting the economy (we are back to point A), suppose that there is a change in the supply of labor so that NS = 5 + 2w (All else remains as in part (a)). (In particular, A = 10 and K = 10.) Find the new levels of the equilibrium real wage rate, the full employment level of employment, and the full-employment level of output for this economy and label on your diagrams as point D.(g) Explain exactly why the profit maximizing level of labor has changed given the change in labor supply. Again be very specific with your answer as in using numbers. Begin your answer with: At the same level of labor input N* = (what it was at point A), the firm is no longer.............h) Give two well supported answers as to why Ns might have changed as it did in part (d) above.

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