304L Homework 6 Solutions

# 304L Homework 6 Solutions -...

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Economics 304L: Principles of Macroeconomics Spring 2010 Sadler Homework 6 Solutions 1. Note that the “gross” growth rate for some variable like real GDP, Y , can be written as ೟షభ ൌ1൅ ݃ , where ݃ is the “net” growth rate (for example, 3 percent per year, so the gross growth rate would be 1.03). Let the equation of exchange (or “quantity equation”) for year t as ܯ ܸ ൌܲ ܻ . a. Noting that in the previous year the equation of exchange can be written as M ୲ିଵ V ୲ିଵ ൌP ୲ିଵ Y ୲ିଵ , write the quantity equation in terms of the growth rates of the four variables and show that the approximate final answer is g m ൅g v ൌπ൅g y . Hint: for any economy under normal circumstances, the product of two growth rates, such as g m g v is approximately zero . For example, assume that g m ൌ.05 and g v ൌ.02 , then g m g v ൌ ሺ.05ሻሺ.02ሻ ൌ .001 , which is very close to zero, so we will assume that it is exactly zero. Just divide the quantity equation for year t by that for year t 1: ࢚ି૚ ࢚ି૚ ۾ ܜି૚ ܇ ܜି૚ ࢚ି૚ ࢚ି૚ ۾ ܜି૚ ܇ ܜି૚ ሺ૚൅ࢍ ሻሺ૚൅ࢍ ሻ ൌ ሺ૚൅࣊ሻሺ૚൅ࢍ Where the gross growth rate in the price level ۾ ܜష૚ is one plus the rate of inflation, . ૚൅ࢍ ൅ࢍ ൅ࢍ ൌ૚൅࣊൅ࢍ ൅࣊ࢍ According to the hint given in the problem, the two product terms on each side of the equation are approximately zero, so we set them to zero. Canceling the ones on both sides leaves ൅ࢍ ൌ࣊൅ࢍ b. Imposing the assumptions of the quantity theory onto the equation, demonstrate Milton Friedman’s dictum that “Inflation is always and everywhere a monetary phenomenon.” According to the quantity theory as we discussed in class, velocity is constant, so its growth rate is zero: ൌ૙ so ൌ࣊൅ࢍ The quantity theory is part of the classical school of macroeconomics, which asserts that real variables, such as real GDP, Y , cannot be influenced by nominal variables such as the money supply. Therefore, should be considered fixed and not influenced by changes in the growth rate of the money supply, .

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Economics 304L: Principles of Macroeconomics Spring 2010 Sadler Putting all of this together, if the Fed increases or decreases the growth rate of the money supply,
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## This note was uploaded on 12/17/2010 for the course ECO 33530 taught by Professor Sadler during the Spring '10 term at University of Texas at Austin.

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304L Homework 6 Solutions -...

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