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Fall 2009 Midterm Exam Solutions

Fall 2009 Midterm Exam Solutions - Department of Economics...

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Department of Economics University of Maryland Economics 325 Intermediate Macroeconomic Analysis Midterm Exam – Suggested Solutions Professor Sanjay Chugh Fall 2009 NAME: Each problem’s total number of points is shown below. Your solutions should consist of some appropriate combination of mathematical analysis, graphical analysis, logical analysis, and economic intuition, but in no case do solutions need to be exceptionally long. Your solutions should get straight to the point – solutions with irrelevant discussions and derivations will be penalized. You are to answer all questions in the spaces provided. You may use one page (double-sided) of notes. You may not use a calculator. TOTAL PART 1 / 50 TOTAL PART 2 / 50 TOTAL / 100
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1 Problem 1: Core Inflation and Non-Core Inflation in the Two-Period Economy (30 points). Two distinct measures of inflation – called core inflation and non-core inflation – generally attract attention by policy-makers and the media. The core inflation rate is the rate of growth of prices of so-called “core goods” (such as food, clothing, and shelter), while the non-core inflation rate is the rate of growth of prices of so-called “non-core goods” (generally energy items). Consider our usual two-period economy (with no government), in which the representative consumer has no control over his nominal income. Rather than there being only one “type” of good the consumer purchases each period, however, suppose that each period there are two “types” of goods: core good and non-core goods. The lifetime utility function of the representative consumer is ! " ! " ! " ! " ! " 1 1 2 2 1 1 2 2 , , , ln ln ln ln CORE NONCORE CORE NONCORE CORE NONCORE CORE NONCORE u c c c c c c c c # $ $ $ , where ln stands for the natural logarithm, 1 CORE c stands for consumption of core goods in period 1, 1 NONCORE c stands for consumption of non-core goods in period 1, and similarly for 2 CORE c and 2 NONCORE c . The representative consumer begins period one with zero assets (i.e., A 0 = 0). The period-by- period budget constraints of the representative consumer are thus 1 1 1 1 1 1 2 2 2 2 2 2 1 (1 ) CORE CORE NONCORE NONCORE CORE CORE NONCORE NONCORE P c P c A Y P c P c A Y i A $ $ # $ $ # $ $ where 1 CORE P denotes the nominal price of core goods in period 1, 1 NONCORE P denotes the nominal price of non-core goods in period 1, and similarly for 2 CORE P and 2 NONCORE P . As usual, 1 Y and 2 Y denote nominal income in periods 1 and 2, respectively, and i is the nominal interest rate. Finally, we can construct as usual the representative consumer’s nominal lifetime budget constraint, which here is: 2 2 2 2 2 1 1 1 1 1 1 1 1 CORE CORE NONCORE NONCORE CORE CORE NONCORE NONCORE P c P c Y P c P c Y i i i $ $ $ # $ $ $ $ This nominal LBC has the same interpretation as always: the PDV of all lifetime nominal consumption (which here takes into account both consumption of core and non-core goods) is equal to the PDV of all lifetime nominal income. That is, in a lifetime sense, all consumption spending equals all income regardless of “how many” goods there are to purchase.
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