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I. Hakan Yetkiner http://www.hakanyetkiner.com/ Izmir University of Economics Department of Economics ECON 300 Advanced Macroeconomics 30 November 2011 Dr. Yetkiner MOCK EXAM Key to Midterm Exam 1. (20 Points) Calculate the GDP of Farmland, a fictitious economy whose numbers are listed below. Do so using all three methods (value added approach, income approach, and expenditure approach). FarmLand, year 2000 Farmer Jones, (private firm) Corn sold to Govt Corn sold to Singapore Corn sold to FoodCo, Inc Paid workers Tax on profit Farmland Govt Taxes Purchase of Corn Wages Purchase of Corn Flakes Value-added Approach: Expenditure Approach: Income Approach: $25 $25 $20 $40 $15 $50 $25 $10 $15 FoodCo, Inc Corn Flakes Sold to Consumers Corn Flakes Sold to Japan Corn Flakes Sold to Government Corn bought from Farmer Jones Corn Inventory Beginning of Year End of Year Salt bought from Egypt Paid workers Tax on Profit Households Taxes on wage income 70 + [125-30-10] +10= 165 100 + -10 + 50 + (35-10) = 165 70 + 55 + 40 = 165 W Π TA Grading: 5 points each 1 $100 $10 $15 $20 $10 $0 $10 $20 $25 $10 5 points 5 points 5 points I. Hakan Yetkiner http://www.hakanyetkiner.com/ Izmir University of Economics Department of Economics 2. (10 Points-Partial Equilibrium) Suppose that utility function u of a representative agent is u c (3 / 4) l (1/ 4) , where c is consumption of physical goods and l is consumption of leisure. Suppose further that w 3 , 24 , and h 24 . Find the optimal values of c and l . Initially, the Lagrangian is: L C(3/4)l (1/ 4) C 3l 72 24. The first order conditions are: L (Equation 1) 0 (0.75)C-0.25l 0.25 0 C L (Equation 2) (3 points) 0 (0.25)C0.75l 0.75 3 0 l L (Equation 3) 0 C 3l 96 0 From the first two first-order conditions (i.e., from (1) and (2)), we obtain: (0.75)C -0.25l 0.25 C 9 l . Using this result in the third first-order condition: 0.75 0.75 3 (0.25)C l 9 l 3l 96 l * 8 c* 72 . 2 I. Hakan Yetkiner http://www.hakanyetkiner.com/ Izmir University of Economics Department of Economics 3. (25 Points- General Equilibrium) Suppose that utility function u of a representative agent is u c (1/ 4) l (3 / 4) , where c is consumption of physical goods and l is consumption of leisure. Suppose that production technology is represented by y (0.5) K 0.25 N 0.75 where K 16 is the physical capital stock and N is labor. We assume that h 24 , h l N and that there is no government in the economy (use w and to denote the real wage and profits, respectively). Find the optimal values of c , l , N , y , w , , and u under the competitive equilibrium assumption. This is a General Equilibrium Model. Let us start from the household’s problem. The Lagrange is: L C(1/4)l (3 / 4) C wl wh . The first order conditions are: L 0 (0.25)C -0.75l 0.75 0 C L 0 (0.75)C 0.25l 0.25 w 0 l L 0 C wl wh 0 (Equation 1) (Equation 2) (3 points) (Equation 3) From the first two first-order conditions (i.e., from (1) and (2)), we obtain: (0.25)C-0.75l 0.75 wl C 0.25 0.25 (0.75)C l w 3 Using this result in the third first-order condition: wl 4wl 3 3 3 . In order to solve wl wh wh l h l 18 3 3 4 4w 4w the model, we need labor supply, which may be obtained directly from N l 24 : 3 3 s . N s 24 l N s 24 18 N 6 4 w 4w We cannot solve the problem unless π is determined. For this, let us look at the production side. From the firm’s profit maximization problem: 1 (0.5) K 0.25 N 0.75 d 0.75 0.25 wN (0.75) N 0.25 w 0 N d . dN w We need to also calculate profits: w 1 ( N 0.25 w) N ( w) N (0.333) wN w N . 0.75 3 3 I. Hakan Yetkiner http://www.hakanyetkiner.com/ Izmir University of Economics Department of Economics Now we have enough information to solve the general equilibrium problem. First, use the profit equation in the labor supply: 1 1 w N 0.25 3 0 . 75 Ns 6 3 N s 6 (0.25) N 6 (0.25) 4 w w Given that N s N d at equilibrium, N 6 (0.25) N (1.25) N 6 N * 4.8 (2 points) 1 0.75 0.25 Using this information at N d implies w* 0.506 . w (2 points) The rest can be calculated by substitution: * 0.8096 (2 points) (2 points) (2 points) (2 points) (3 points) l 19.2 C * 3.23 y * 3.23 * u * 10.51 4 I. Hakan Yetkiner http://www.hakanyetkiner.com/ Izmir University of Economics Department of Economics 4. (15 Points) Suppose that the government decides to increase taxes. Using the general equilibrium model developed in chapter 5, determine the effects this has on aggregate output, consumption, employment, and the real wage. Hint: Do not forget to draw a figure and discuss in detail the impact of the exogenous shock. p.161, figure 5.6 (Important Note: page numbers and/or figure numbers may change depending on the edition of the textbook) 5. (15 Points) Suppose that Robinson Crusoe has a two-period life in a partial equilibrium framework. Furthermore, we assume that Mr. Crusoe show “borrower” behavior. Analyze the impact of an increase in the interest rate on current and future consumption and saving. p. 286 in chp.8, figure 8.14 (Important Note: page numbers and/or figure numbers may change depending on the edition of the textbook) 6. (15 Points-Partial Equilibrium) Suppose that Daniel has income of when he is young and when he is old. The real interest rate is r 0.1 . The overall c1 1 1 c12 1 utility function of Daniel is U 1 , where 2 . Find the optimal 1 1.21 1 values of c1 , c 2 and s . This is a Partial Equilibrium Model. The household’s problem c 1 1 c21 1 c 990 L c1 2 900 . The first order conditions are: 1 1.1 1.1 1.21 1 1 1 L 0 c1-2 0 c1 (Equation 1) 5 is: I. Hakan Yetkiner http://www.hakanyetkiner.com/ Izmir University of Economics Department of Economics L 1 -2 0 0 c 2 c2 1.1 1.21 c L 0 c1 2 1800 0 1.1 (Equation 2) (3 points) (Equation 3) From the first two first-order conditions (i.e., from (1) and (2)), we obtain: c2 0.953c1 c1* 964.44 0.953c1 1800 1.1 (2 points) c2* 919.11 s* 64.44 (2 points) (2 points) Using this result in the third first-order condition: c1 6