Explanation Given Information: For national disposable income y , the national consumption function is represented as, C ( y ) = 2 ( y + 1 ) 1 2 + 0.4 y + 4 . Formula used: According to the power rule, if f ( x ) = x n , then, f ′ ( x ) = n x n − 1 According to the property of differentiation, if a function is of the form, g ( x ) = c f ( x ) , then, g ′ ( x ) = c f ′ ( x ) According to the property of differentiation, if a function is of the form f ( x ) = u ( x ) + v ( x ) , then, f ′ ( x ) = u ′ ( x ) + v ′ ( x ) The derivative of a constant value, k , is d d x ( k ) = 0 According to the property of differentiation, if a function is of the form y = u n , where u = g ( x ) , d y d x = n u n − 1 d u d x According to the property of differentiation, if a function is of the form y = u n , where u = g ( x ) , d y d x = n u n − 1 d u d x Calculation: Consider the provided consumption function, C ( y ) = 2 ( y + 1 ) 1 2 + 0.4 y + 4 The marginal propensity to consume is found by differentiating the consumption function with respect to y . Consider ( y + 1 ) to be u , C ( y ) = 2 u 1 2 + 0.4 y + 4 Differentiate both sides with respect to y , d C d y = d d y ( 2 u 1 2 + 0.4 y + 4 ) = d d y ( 2 u 1 2 ) + d d y ( 0

Mathematical Applications for the Management, Life, and Social Sciences

12th Edition

ISBN: 9781337625340

Author: Ronald J. Harshbarger, James J. Reynolds

Publisher: Cengage Learning

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Chapter 9.7, Problem 39E

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To calculate: The marginal propensity to consume, dCdy, for the consumption function, C(y)=2(y+1)12+0.4y+4.

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Chapter 9.7, Problem 38E

Chapter 9.7, Problem 40E

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Chapter 9 Solutions

Mathematical Applications for the Management, Life, and Social Sciences

Ch. 9.1 - 1. Can exist if is undefined? Ch. 9.1 - 2. Does exist if ? Ch. 9.1 - 3. Does Ch. 9.1 - 4. If , does exist? Ch. 9.1 - 5. Let (a) Does (b) Find . Ch. 9.1 - 6. Evaluate the following limits (if they...Ch. 9.1 - Prob. 7CP Ch. 9.1 - Prob. 8CP Ch. 9.1 - Prob. 9CP Ch. 9.1 - Prob. 10CP

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The marginal propensity to consume, d C d y , for the consumption function, C ( y ) = 2 ( y + 1 ) 1 2 + 0.4 y + 4 .

Solution Summary: The author calculates the marginal propensity to consume for the consumption function, 1(y+1) 0.4y+4.

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To calculate: The marginal propensity to consume, dCdy, for the consumption function, C(y)=2(y+1)12+0.4y+4.

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Chapter 9 Solutions