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##### ECON 3102 Intermediate Macroeconomics

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ECON 3102 Intermediate Macroeconomics;Problem Set 1;This problem set is due Monday February 14 at the beginning of the class. Go over;Handout 1 and Chapter 4 before you start.;1;Nominal GDP v.s. Real GDP (20 points);In this question we ask you to compute the GDP for a hypothetical economy that produces two;goods (computers and gasoline). The prices and quantities produced in each year are provided;in the following table;2006;Prices;Computers;Gasoline;Quantities;Computers;Gasoline;2007;2008;$2 000;$1 900;$1 200;$50gal. $100gal. $400gal;10;100 gal.;16;120 gal.;40;110 gal.;a. Compute the nominal GDP for each of the three years.;b. Compute the real GDP for each of the three years, taking 2006 as your base year.;c. How does the real GDP in 2006 compare to the nominal GDP in 2006 when 2006 is;used as the base year?;d. Based on your calculations, comment on the economic well-being of the above two-good;economy. Have things improved over time for this country (in Real GDP terms)?;e. State three problems of measuring Real GDP using the above approach.;1;2;Perfect Substitute and Perfect Complement Utility (20;points);Consider the consumer optimization problem we have studied in class. Suppose that consumption good and leisure are perfect substitutes, namely preferences of the consumer are represented;by the utility function;() = +;where and are positive constants.;a. Show what the consumers indierence curves look like and determine both graphically;and algebraically what consumption bundle () the consumer chooses. Show that optimal;consumption bundle depends on the relationship between and, and explain why.;b. Now suppose that the utility function is given by;() = min();where is a positive constant.;Determine the optimal consumption bundle () in terms of,,, and.;Hint: Optimal consumption bundle will be on the line = This is the example we did in;class and also in the textbook.;3;Cobb-Douglas Utility (30 points);Consider again the problem of the representative consumer whose preferences given by the utility;function;() =;where is a positive constant.;Determine the optimal consumption bundle () in terms of,,, and, i.e.;obtain the closed-form solutions for and.;2;4;Numerical Exercises (30 points);a. Consider a representative consumer whose preferences over consumption and leisure are;given by the utility function () = 12 12. Assume that she has a total of = 18;hours which she can use for leisure or she can work for the wage rate = 6. Finally;assume that she enjoys a dividend income = 36 and has to pay taxes = 24.;Determine the optimal consumption bundle ().;b. Redo part (a) but now set = 40 and = 18. How do the optimal consumption and;optimal leisure change relative to your answer in part (a)?;c. Redo part (a) but now set = 8. How do the optimal consumption and optimal leisure;change relative to your answer in part (a)?;3

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