Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 5: Problem 163

Suppose that John's \(\mathrm{MPC}\) is constant at \(4 / 5\). If he had no income at all, he would have to borrow $$\$ 2,000$$ to meet all his expenses. Graph John's consumption function and write it out algebraically. Using the formula for John's consumption function, find his break-even point.

Short Answer

Expert verified
John's consumption function is \(C = 2000 + \frac{4}{5}Y\). By graphing this function with Income (Y) on the horizontal axis and Consumption (C) on the vertical axis, we can visualize John's spending behavior. To find the break-even point, set \(C = Y\), which yields the equation: $$ Y = 2000 + \frac{4}{5}Y $$ Solving for \(Y\) gives us a break-even income level of \(Y = 10,000\). At this income level, John's consumption will also be $10,000, and he will not need to borrow any more money to meet his expenses.

Step by step solution

01

Determine Autonomous Consumption

Since John would have to borrow \(2,000 if he had no income, we can assume that his autonomous consumption, \)a\(, is equal to \)2,000.
02

Write the Consumption Function

John's consumption function can be written as: $$C = 2000 + \frac{4}{5}Y$$
03

Graph the Consumption Function

To graph John's consumption function, create a coordinate plane with Income (Y) on the horizontal axis and Consumption (C) on the vertical axis. 1. Plot the point (0, 2000) on the graph, which represents John's autonomous consumption. 2. Use the slope (MPC) of \(4/5\) to identify another point on the graph. For example, if John has an income of \(5,000, his consumption would be: \)C = 2000 + \frac{4}{5}(5000) = 6000$. 3. Connect the points on the graph with a straight line to represent John's consumption function.
04

Find the Break-even Point

The break-even point occurs when John's consumption equals his income. We can set \(C = Y\) and solve for \(Y\): $$ Y = 2000 + \frac{4}{5}Y $$ Subtract \(\frac{4}{5}Y\) on both sides to isolate \(Y\) term: $$ Y - \frac{4}{5}Y = 2000 $$ Combine like terms and solve for \(Y\): $$ \frac{1}{5}Y = 2000 $$ Multiply both sides by 5 to get the break-even income level: $$Y = 10,000 $$ John's break-even point occurs when his income is \(10,000. When John earns this amount, his consumption will also be \)10,000, and he will not need to borrow any more money to meet his expenses.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Assume that in a given year, consumption and saving schedules are as given (columns 1 through 3 in billions of dollars). $$ \begin{array}{|c|c|c|} \hline \begin{array}{c} \text { (1) } \\ \text { Level of output and } \\ \text { income } \\ (\mathrm{NNP}=\mathrm{D} 1) \end{array} & \begin{array}{c} (2) \\ \text { Consumption } \end{array} & \begin{array}{c} (3) \\ \text { Saving } \end{array} \\ \hline \$ 510 & 480 & 30 \\ \hline 530 & 495 & 35 \\ \hline \end{array} $$ a) Determine the average propensity to consume \((\mathrm{APC})\) and the average propensity to save (APS). b) Compute the marginal propensity to consume (MPC) and the marginal propensity to save (MPS).

Keynesian economists claim that investment is the most volatile component of private spending. If this is so, why is the investment function, as shown, drawn as a straight line, rather than as an erratic curve?

Consider the given aggregate consumption schedule. $$ \begin{array}{|c|c|c|} \hline \begin{array}{c} \text { Income } \\ \text { (in billions) } \end{array} & \begin{array}{c} \text { Consumption } \\ \text { (in billions) } \end{array} & \begin{array}{c} \text { Savings } \\ \text { (in billions) } \end{array} \\ \hline \$ 600 & \$ 600 & 0 \\ \hline 700 & 660 & 40 \\ \hline 800 & 720 & 80 \\ \hline 900 & 780 & 120 \\ \hline \end{array} $$ Comment on the MPC MPS, APC and APS in this situation.

Contrast the Keynesian, or modern, economic theory of saving and investment with the classical economic view.

Suppose that John's MPC is constant at \(3 / 4\). If his breakeven point occurs at $$\$ 7,000$$, how much will John have to borrow when his income is $$\$ 3,000 ?$$
See all solutions

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free