Suppose that the Fed\'s inflation target is 2%, potential output growth is 3.5%,

Question

Suppose that the Fed's inflation target is 2%, potential output growth is 3.5%, and velocity is a function of how much the interest rate differs from 5%: % triangle v=0.5x(i-5) Suppose that a model of the economy suggests that the real interest rate is determined by the equation: r =8.5-% triangle Y where Y is the level of output, so %triangleY is the growth rate of output. Suppose that people expect the Fed to hit its inflation target. A: Calculate the optimal money growth rate needed for the Fed to hit its inflation target in the long run.

Explanation / Answer

Use the equation that i = r + ?e; combine that with the equation that r = 8.5 ? %?Y and that people will expect the Fed to hit its inflation target, so ?e = ?T = 2 percent, and that output growth is expected to equal the rate of potential output growth, %?Y = %?Y* = 3.5%, to get

First Step: %?V = 0.5 Ý (i ? 5)
= 0.5 Ý (r + ?e ? 5)
= COMPLETE THIS PART TO GET %?V AND SOLVE FOR SECOND STEP

Second Step: %?M = ?T + %?Y* ? %?V
(REMEMBER THAT ?T AND %?Y ARE GIVEN IN THE PROBLEM )

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