Explanation Given Information: The consumption is $12 billion when disposable income is $0 billion and if the marginal propensity to save is d S d y = 0.2 − 1 y + 1 . Formula used: The power rule of integration is; The integration of function f ( x ) = x n is given by; ∫ x n d x = x n + 1 n + 1 + c n ≠ − 1 The integration of function f ( x ) = 1 a x + b is given by; ∫ 1 a x + b d x = ln ( a x + b ) a + c Here c is any arbitrary constant. The sum rule is; ∫ f ( x ) ± g ( x ) d x = ∫ f ( x ) d x ± ∫ g ( x ) d x Calculation: Consider the marginal propensity to save is; d S d y = 0.2 − 1 y + 1 And the marginal propensity to save is 1 minus the marginal propensity to consume, d S d y = 1 − d C d y d C d y = 1 − d S d y = 1 − ( 0.2 − 1 y + 1 ) = 0.8 + 1 y + 1 And the consumption is $12 billion when disposable income is $0 so; d C 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 12.4, Problem 25E

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To calculate: The national consumption function If consumption is $12 billion when disposable income is $0 billion and if the marginal propensity to save is dSdy=0.2−1y+1.

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Chapter 12.4, Problem 24E

Chapter 12.4, Problem 26E

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Chapter 12 Solutions

Mathematical Applications for the Management, Life, and Social Sciences

Ch. 12.1 - 1. True or false: (a) (b) Ch. 12.1 - Prob. 2CP Ch. 12.1 - 1. If what is Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E Ch. 12.1 - Prob. 5E Ch. 12.1 - Evaluate the integrals in Problems 5-28. Check...Ch. 12.1 - Prob. 7E Ch. 12.1 - Evaluate the integrals in Problems 5-28. Check...

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The national consumption function If consumption is $12 billion when disposable income is $0 billion and if the marginal propensity to save is d S d y = 0.2 − 1 y + 1 .

Solution Summary: The author calculates the national consumption function based on the marginal propensity to save and the power rule of integration.

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To calculate: The national consumption function If consumption is $12 billion when disposable income is $0 billion and if the marginal propensity to save is dSdy=0.2−1y+1.

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Chapter 12 Solutions