   Chapter 11.4, Problem 97E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

Money Stock Exercises 97–100 are based on the following demand function for money (taken from a question on the GRE Economics Test): M d = 2 × y 0.6 × r − 0.3 × p , Where M d = demand for nominal money balances (money stock y = real income r = an index of interest rates p = an index of prices. These exercises also use the idea of percentage rate of growth:Percentage rate of growth of M = Rate of growth in  M M = d M / d t M . (From the GRE Economics Test) If the interest rate and price level are to remain constant while real income grows at 5% per year, the money stock must grow at what percent per year?

To determine

To calculate: The percent per year for the money stock to grow if the interest and price level are to remain constant while real income grows 5% per year and the demand function for money is Md=2×y0.6×r0.3×p.

Explanation

Given Information:

The interest and price level are to remain constant while real income grows 5% per year.

GRE Economic Test:

Md=2×y0.6×r0.3×p

Where,

Md=for nominal money balances (money stock)y=real incomer=an index of interest ratesp=an index of prices

percentage rate of growth of M=Rate of growth of MM=dM/dtM

Formula used:

Derivative of function f(x)=(u)n using chain rule is f'(x)=ddx(u)n=nun1dudx, where u is the function of x.

Calculation:

Consider the function, Md=2×y0.6×r0.3×p

Assume r and p are fixed,

dMdt=ddt(2×y0

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