Question

A. A. Wingit, a noted professor of economics, claims to have derived a consumption function for the U.S. for 1980 . Prof. Wingit claims that the U.S. marginal propensity to consume will be constant for all ranges of income at \(.9\). The professor also claims that if no income were earned by anyone in the entire nation, $$\$ 100$$ billion would need to be "dissaved". Graph Prof. Wingit's consumption function. What is his break-even point?

Short answer

The consumption function derived by Prof. Wingit is given by \(c = 0.9Y - 100\), with a slope of 0.9 and intersects the y-axis at -\(100\) billion. The break-even point occurs when the income level is \(1000\) billion.

Step-by-step solution

Write down the consumption function equation

Prof. Wingit claims that the marginal propensity to consume (MPC) is constant at 0.9, which means for every dollar earned, 90 cents is spent on consumption. This can be represented as: \(c = MPC * Y + C_0\), where c is the consumption, Y is the income, MPC is the marginal propensity to consume (0.9 in this case), and \(C_0\) is the autonomous consumption (consumption when income is zero).

Calculate the autonomous consumption

Prof. Wingit also claims that if no income were earned by anyone, \(100 billion would be dissaved. Since dissaving means negative savings, it implies that people would borrow to consume. Therefore, the autonomous consumption is -\)100 billion: \(C_0 = -100\)

Insert the values into the consumption function equation

Now that we have the values for MPC and \(C_0\), we can write the consumption function formula as: \(c = 0.9Y - 100\)

Graph the consumption function

To graph the consumption function \(c = 0.9Y - 100\), you can plot the equation on a graph with Y (income) on the x-axis and c (consumption) on the y-axis. The line will have a slope of 0.9 and intersects the y-axis at -$100 billion.

Find the break-even point

The break-even point is when consumption is equal to income, i.e., c = Y. Let's solve for Y in the equation: \(Y = 0.9Y - 100\) \(0.1Y = 100\) \(Y = 1000\) So, the break-even point occurs at $1000 billion. In conclusion, the consumption function derived by Prof. Wingit is given by \(c = 0.9Y - 100\). The graph of the function shows a slope of 0.9 and intersects the y-axis at -\(100 billion. The break-even point happens at an income level of \)1000 billion.

Key concepts

Marginal Propensity to Consume

The Marginal Propensity to Consume (MPC) plays a pivotal role in understanding consumer behavior in economics. Simply put, MPC measures how much consumption changes with a change in income. If MPC is 0.9, it means that for every extra dollar of income earned, individuals will, on average, spend 90 cents on goods and services.

Here are a few key points to remember about MPC:

• A higher MPC means that consumers are likely to spend a significant portion of any additional income, stimulating economic growth.
• Conversely, a lower MPC suggests that consumers might save more rather than spend the additional income.
• MPC is crucial for policymakers who are designing financial models or considering changes in taxation or government spending.

Understanding the MPC helps in predicting trends in consumer spending and how changes in income impact overall economic health. In the case of Prof. Wingit's exercise, the MPC is constant at 0.9, highlighting a high tendency of consumers to spend additional income.

Autonomous Consumption

Autonomous consumption refers to the level of consumption that would occur when income is zero. This concept holds significance because even without income, individuals or households still need to spend to maintain basic living standards.

For the exercise provided by Prof. Wingit, autonomous consumption is represented by \(C_0 = -100\) billion. This negative value implies dissaving, meaning people would need to borrow or dip into their savings in order to cover their consumption needs. Here are some insights on autonomous consumption:

• It is considered the base level of consumption, required to meet essentials regardless of income level.
• A negative autonomous consumption value indicates necessary borrowing or use of savings.
• Policy measures can affect autonomous consumption, especially in terms of providing subsidies or welfare benefits.

Understanding autonomous consumption helps in analyzing how much of the consumption is independent of income changes, thereby providing insights into consumer needs and economic resilience during economic downturns.

Break-even Point

The break-even point in a consumption function is where income equals consumption, meaning that everything earned is spent without affecting savings or resulting in dissaving. In Prof. Wingit's analysis, we found the break-even point by setting consumption equal to income. Mathematically, the equation is solved as follows:

Given the consumption function \(c = 0.9Y - 100\), we set \(Y = c\) to find:

• \(Y = 0.9Y - 100\)
• Rearranging gives \(0.1Y = 100\)
• Solving for \(Y\), we find \(Y = 1000\) billion.

This means the economy "breaks even" when national income is $1000 billion. At this point, every dollar of income earned is spent on consumption without saving or needing to borrow. Understanding the break-even point is important for evaluating economic stability and determining at what income level the economy can maintain equilibrium without accumulating debt.