Explanation Given information: The function, M d = ( 2 ) × ( y ) 0.6 × ( r ) − 0.3 × ( p ) represents the demand function for money where M d represents the money stock or the demand for nominal money, y represents real income, r represents the interest rate and p represents the price level. The real income increases although the money stock and the price level remains fixed. Formula used: The derivative of function f ( x ) = u n using the chain rule is f ′ ( x ) = d d x ( u n ) = n u n − 1 d u d x , where u is the function of x . Product rule of derivative of differentiable functions, f ( x ) and g ( x ) is d d x [ f ( x ) ⋅ g ( x ) ] = f ′ ( x ) ⋅ g ( x ) + f ( x ) ⋅ g ′ ( x ) . Constant multiple rule of derivative of function f ( x ) is f ' ( c x ) = c f ' ( x ) where c is constant. Derivative of function y with respect to x using the chain rule in differential notation is d y d x = d y d u d u d x , where y is the differentiable function of u and u is the differentiable function of x . Calculation: Consider the function, M d = ( 2 ) × ( y ) 0.6 × ( r ) − 0.3 × ( p ) As the real income increases while the money stock and the price level remains fixed, the variable M d and p remains constant. First, find d r d y to calculate the rate of change in interest rate. Take d d y of both sides of the equation, d d y ( M d ) = d d y [ ( 2 ) × ( y ) 0.6 × ( r ) − 0.3 × ( p ) ] Apply the constant multiple rule, 0 = 2 p d d y [ ( y ) 0.6 ( r ) − 0.3 ] Now, apply the product rule of derivative, 0 = 2 p ( d d y ( y 0.6 ) ⋅ r − 0.3 + y 0.6 ⋅ d d y ( r − 0

Student Solutions Manual for Waner/Costenoble's Finite Math and Applied Calculus, 7th

7th Edition

ISBN: 9781337275972

Author: Waner, Stefan; Costenoble, Steven

Publisher: Cengage Learning

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Chapter 11.6, Problem 61E

To determine

To calculate: The rate at which the interest rate changes when the real income increases although the money stock and the price level remains fixed. The demand function for the money is given by:

Md=(2)×(y)0.6×(r)−0.3×(p)

Where, Md represents the money stock or the demand for nominal money, y represents real income, r represents the interest rate and p represents the price level.

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Chapter 11.6, Problem 60E

Chapter 11.6, Problem 62E

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Solution Summary: The author calculates the rate at which the interest rate changes when the real income increases although the money stock and the price level remain fixed.

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