Explanation Given information: The national consumption is $ 6.04 billion The disposable income is $ 0 and The marginal propensity to save is d S d y = 0.96 − ln ( y + 1 ) y + 1 . Formula used: Marginal propensity to consume: Marginal propensity to consume d C d y is defined as one minus Marginal propensity to save d S d y . d C d y = 1 − d S d y National consumption function: The national consumption function C is defined as the integration of the marginal propensity f ′ ( y ) . C = ∫ f ′ ( y ) d y = f ( y ) + K Integral formula, ∫ x n d x = x n + 1 n + 1 + K Calculation: It is provided that the marginal propensity to save is: d S d y = 0.96 − ln ( y + 1 ) y + 1 . Consider the formula: d C d y = 1 − d S d y Substitute 0.96 − ln ( y + 1 ) y + 1 for d S d y and evaluate the marginal propensity to consume, d C d y = 1 − ( 0.96 − ln ( y + 1 ) y + 1 ) = 0.04 + ln ( y + 1 ) y + 1 Thus, f ′ ( y ) = 0.04 + ln ( y + 1 ) y + 1 Consider the formula: C = ∫ f ′ ( y ) d y = f ( y ) + K Substitute 0.04 + ln ( y + 1 ) y + 1 for f ′ ( y ) in above formula, C = ∫ ( 0.04 + ln ( y + 1 ) y + 1 ) 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

See similar textbooks

Concept explainers

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …

Videos

Question

Chapter 12.4, Problem 28E

To determine

To calculate: The national consumption function if the national consumption is $6.04 billion and the disposable income is $0 and if the marginal propensity to save is dSdy=0.96−ln(y+1)y+1.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 12.4, Problem 27E

Chapter 12.4, Problem 29E

Students have asked these similar questions

Can you evalutate the following summation:∑_{y=1}^{x} 2 / ((x + y - 1)(x + y + 1))

A retail chain is interested in determining whether a digital video point-of-purchase (POP) display would stimulate higher sales for a brand advertised compared to the standard cardboard point-of-purchase display. To test this, a one-shot static group design experiment was conducted over a four-week period in 100 different stores. Fifty stores were randomly assigned to the control treatment (standard display) and the other 50 stores were randomly assigned to the experimental treatment (digital display). Compare the sales of the control group (standard POP) to the experimental group (digital POP). What were the average sales for the standard POP display (control group)? What were the sales for the digital display (experimental group)? What is the (mean) difference in sales between the experimental group and control group? List the null hypothesis being tested. Do you reject or retain the null hypothesis based on the results of the independent t-test? Was the difference between the…

Can you evaluate the following summation:∑_{k=1}^{n} (4log(n+k) + 4k)

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...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The national consumption function if the national consumption is $ 6.04 billion and the disposable income is $ 0 and if the marginal propensity to save is d S d y = 0.96 − ln ( y + 1 ) y + 1 .

Solution Summary: The author calculates the national consumption function if the disposable income is 0 and the marginal propensity to save is

Concept explainers

Videos

To calculate: The national consumption function if the national consumption is $6.04 billion and the disposable income is $0 and if the marginal propensity to save is dSdy=0.96−ln(y+1)y+1.

Want to see the full answer?

Chapter 12 Solutions