All the questions

Exercise #1. A firm produces output using the technology y = 7 1.000 where capital, K, is measured in machine-hours, labor, L, is measured in person-hours, and y denotes the yearly output. The hourly wage rate un = 10, and the hourly rental rate of capital is Wk = 20. (a) Show that this technology displays increasing returns to scale. (b) Compute the marginal products of labor and capital. (c) Suppose that at the end of 1999 the firm has signed a contract to rent K = 1,000 machine hours over the course of the year 2000. Derive the firm's short run cost function in the year 2000. (d) What is the firm's short run marginal cost function? What is the firm's short run average cost function? At which point do these two curves intersect? (e) On a diagram plot the firm's short run average and marginal cost curves. Exercise #2. The aggregate labor supply in the state of Bahnanas is Ls = 2,000ur, where w is the hourly wage, measured in Bahnanas $ and L, denotes the number of person- hours supplied by the workers of Bahananas in a year. The aggregate labor demand in the state of Bahananas is La = 12,000 - 2,000w. where La denotes the number of person-hours demanded by the firms of Bahnanas in a given year. (a) Compute the equilibrium hourly wage and the amount of hours worked in a given year. (b) The government of Bahnanas introduces a minimum wage law requiring firms to pay an hourly wage not lower than $4. Compute the equilibrium number of hours worked by the workers of Bahnanas. (c) On a diagram that has the wage rate on the y-axis and the number of hours on the x-axis, plot the labor demand and supply functions and the equilibrium prices and quantities that you found in points (a) and (b). (d) Compute the deadweight loss induced by this policy, and show it on the diagram of point (c). Exercise #3. Short questions. (a) Compute the price and income elasticities of the following demand function Im Id (p.m) = 2p (b) A firm produces output, denoted by y, using the following production function y = 10VL, where L represents the labor input, measured in person-hours. The unit price of output is $10. Let w denote the hourly wage rate. Compute and plot on a diagram the inverse labor demand curve for the firm. (c) Explain how it can be possible that as tax rates decrease, government tax revenues increase (i.e. the Laffer curve).Exercise # 1. Andy consumes two goods. food (measured in dollars) and other things (also measured in dollars). Let X be the amount that Andy spends on food in a givea month and let Xy be the amount that Andy spends on other things in a given month. Andy's preferences over consumption bundles (X1,X2) are summarized by the utility function. U (X1,X2) = X1X2. Andy's monthly income is $400 (a) [10 pts.] What is Andy's optimal consumption bundle? Show your work. Illustrate your answer with a neat and clear diagram showing Andy's budget line and indifference curves. Label the points at which the budget line intersects the axes and identify the optimal bundle. (b) [10 pts.] Suppose now that the government implements a subsidy program for food. Specif- ically, for each dollar that Andy spends on food, the government will give Andy 30.50 in cash, with the restriction that the total amount of cash that Andy receives from the government cannot exceed $100. In a meat and clear diagram, graph Andy's budget line. Label the points at which the budget line interacts the ases and determine the coordinates of the kink point. Exercise # 2. Barb's preferences over consumption bundles (x.y) are summarized by the following utility function: u (x1, 2) = 16x - 2x" + 4y. where X is the amount of good X that Barb consumes and y is the amount of good y that Barb consumes. Let Py and Py be the prices of goods X and y, respectively. Let m be Barb's income. Barb's goal is to maximize her utility subject to her badget constraint. (a) [10 pts.] Find an algebraic expression for Barb's marginal rate of substitution between goods x and y. Show your work. In addition, give a coincise explanation of the meaning of the marginal rate of substitution. (b) (10 pts.] Suppose that Pe = Py = 2 and m = 24. Use your answer from part (a) to determine Barb's optimal consumption bundle. Show your work (c) (10 pts.] Suppose now that Pa increases to 6, while Py and M remain the same. What are Barb's optimal choices for X and y in this case. Is Barb better or worse off than she was in part (b)? Explain. (d) (10 pts.] How much extra income must Barb be given in order to compensate her for the increase in the price of good X in part (c)? Explain. Exercise # 3. Consider the following statements and say whether they are true or false and why. To get credit you should provide a clear justification for your answers. (a) [4 pts. ] If two goods are perfect complements and the price of one of them increases, the quantity demanded of both goods decreases. (b) [4 pts.] A nonetransitive preference relation _ can be represented by some utility function. (c) |4 pts.) Consider two goods x and y. If preferences are strictly convey, the absolute value of the marginal rate of substitution between X and y is decreasing along an indifference curve as X increases. (d) [4 pts.] The following CobbDouglas utility functions represent two different preference relations: U, (x.y) = 0.3log(x) + 0.6 logly) uj (x.y) = 0.blog(x) + 1.2log(y). (e) [4 pts.] If a consumer is making an optimal choice between two goods & and y, then, independently of his preferences, the following condition must always hold: PL - MRS (Xy) Py (f) [4 pts.] If the following condition holds PE - MRS (X.y) Py then a consumer must be making the optimal choice between X and y, independently of his(d) [10 pts.] How much extra income must Barb be given in order to compensate her for the increase in the price of good x in part (c)? Explain. Exercise #3. Consider the following statements and say whether they are true or false and why. To get credit you should provide a clear justification for your answers. (a) [4 pts.] If two goods are perfect complements and the price of one of them increases, the quantity demanded of both goods decreases. (b) [4 pts.] A non-transitive preference relation > can be represented by some utility function. (e) [4 pts.] Consider two goods x and y. If preferences are strictly convex, the absolute value of the marginal rate of substitution between x and y is decreasing along an indifference curve as x increases. (d) [4 pts.] The following Cobb-Douglas utility functions represent two different preference relations: U1 (x.y) = 0.3 log(x) + 0.6 log(y) U2 (x,y) = 0.6 log(x) + 1.2 log(y)- (e) [4 pts.] If a consumer is making an optimal choice between two goods x and y, then, independently of his preferences, the following condition must always hold: Py Px = MRS (x.y) . (f) [4 pts.] If the following condition holds Px = MRS (x.y) Py then a consumer must be making the optimal choice between x and y, independently of his preferences. (g) [4 pts.] A cigar is a luxury good for a consumer that has Cobb-Douglas preferences over cigars and food. (h) [4 pts.] Consider two goods x and y, with prices px and Py, respectively. A 0.07 percent value tax on these two goods does not affect the relative price of x in terms of y. (i) [4 pts.] The marginal rate of substitution measures the rate at which the market is willing to substitute one good for the other. (i) [4 pts.] An indifference curve represents the collection of all the bundles that a consumer can buy.1 {24 points} Consider the following version of model 5. Except where indicated. variables are expressed in current year terms thus the "t" subscript has been suppressed. Be sure to show your work for all parts. ISGurve: Y=W-c{r-p}+hlx+s Net Exports Nit = its - xi-E Fisher Equation: r = i - tt' Phillips Curve; it = n'+ ipfr - W] + v Ination Expectations: n\" = 11.1 Monetary Rule: I: n + p + [3*{n - 11*] + {1- [31*{Y-YP} [l s p: \"I Endogenous variablesLY, r, Nit. n.rr'.i Exogenous variables: 1'i'\".p.e.E.xiu.v.rt"' (a) a. Derive the dynamic aggregate demand curve. Indicate its slope. (3] b. Determine the dynamic aggregate supply curve and indicate its slope. [3] c. Paul Krugman. [ilivier Blanchard and others have suggested that the inflation target {at} be raised to 4%. What would happen to the paths for output and inflation if monetary policy reflected this new inflation target? {F} d. How would the results In d change if inflation expectations were rational? Part II {12 points each} Answer three of the following questions. Indicate any noteworthy assumptions. 1. Evaluate the quotation at the beginning of the exam. If you believe that it is true. provide evidence to support your assertion. If you believe that it is false. how would you change the statement to make it true? Provide evidence to support your claim. 1 Use Model 4 to determine the effect of an exogenous increase in net exports on GDP, P, L, U, WP and r. Assume if: \"if" . Provide graphics to support your claim. 3. Use Model 5 to determine the paths of output and inflation if there is a positive aggregate supply shock in period t [rec in s [1}. Provide graphics to support your claim. 4. The Iron Triangle or lm possible Trilogy a. In terms of policy making regarding openness of the economy, what three policy options must be jointly considered by macroeconomic policy makers? Explain why the third policy depends upon the choice of the first two. b. In light of the Iron Triangle, why might large countries and small countries make different policy choices