Question

Suppose the consumption function is \(C=0.75 \mathrm{Y}\) and planned investment is 40 . (a) Draw a diagram showing the aggregate demand schedule. (b) If actual output is 100 , what unplanned actions will occur? (c) What is the equilibrium output? (d) Do you get the same answer using planned saving equals planned investment?

Short answer

Equilibrium output is 160, verified by both AD approach and savings-investment equality.

Step-by-step solution

Identify the Aggregate Demand Equation

The aggregate demand (AD) is the sum of consumption (C) and planned investment (I). Here, the consumption function is given as \(C = 0.75Y\) and planned investment is 40. Hence, the aggregate demand equation is \(AD = C + I = 0.75Y + 40\).

Draw the Aggregate Demand Schedule

To draw the AD schedule, plot AD for different values of output (Y). For example, if \(Y = 0\), then \(AD = 40\); if \(Y = 100\), \(AD = 0.75 \times 100 + 40 = 115\); and so on. This forms a straight line on a graph with the intercept at 40 and slope 0.75.

Determine Unplanned Actions at Actual Output

Given actual output \(Y = 100\), calculate the AD: \(AD = 0.75\times 100 + 40 = 115\). Since AD > actual output, there is an unintended decrease in inventories because demand exceeds actual production.

Finding Equilibrium Output

Equilibrium occurs where AD equals actual output \(Y\). Set \(AD = Y\), giving the equation \(0.75Y + 40 = Y\). Solving for \(Y\) results in \(0.25Y = 40\), thus \(Y = 160\). Equilibrium output is 160.

Verify Equilibrium Using Saving Equals Investment

Planned saving can be calculated as \(Y - C = Y - 0.75Y = 0.25Y\). Setting planned saving equal to planned investment (40), we have \(0.25Y = 40\), giving \(Y = 160\). This confirms that equilibrium output using savings equals investment provides the same result.

Key concepts

Consumption Function

The concept of the consumption function is fundamental in understanding aggregate demand. The consumption function is a formula that establishes the relationship between consumption and income in an economy. In our exercise, it is expressed as \(C = 0.75Y\). Here, \(C\) represents consumption, and \(Y\) stands for income or output. The number 0.75 is the marginal propensity to consume, indicating that for every additional dollar of income earned, 75 cents are spent on consumption.
To illustrate:

• If income \(Y\) increases, consumption \(C\) will also rise at a rate proportional to this income growth.
• This relationship forms the basis of many economic models, especially when analyzing the elements of aggregate demand.

The remaining income, represented by the difference between 1 and 0.75 (i.e., 0.25), is saved by households, adding complexity to economic interactions.

Equilibrium Output

Equilibrium output in an economy occurs when total output equals aggregate demand. In our scenario, aggregate demand is the sum of consumption and planned investment, \(AD = 0.75Y + 40\).
We find the equilibrium output by setting aggregate demand equal to actual output \(Y\). This yields \(0.75Y + 40 = Y\). Solving gives \(Y = 160\). This value signifies the level of income where the economy is balanced, and the output produced matches the demand.
This concept is crucial because it informs policymakers about stable output levels, helping avoid unwanted fluctuations in economic activity.

Planned Investment

Planned investment is a key part of aggregate demand and one of its components. It reflects the investment intentions of firms for a given period. In our exercise, planned investment is set at 40 units. This means businesses plan to invest 40 irrespective of the current state of the economy.
Planned investments influence the aggregate demand curve by shifting it. They are considered independent of current output levels and remain constant, thereby providing a predictable component of economic spending. By understanding this concept, students grasp how business expectations and plans contribute to the total economic demand.

Unplanned Actions

Unplanned actions in an economy refer to the unexpected changes in inventory levels that occur when actual output does not equal aggregate demand. In this scenario, if the actual output is 100, then with \(AD = 115\), demand exceeds output, causing an unintended inventory reduction.
This situation hints at disequilibrium, triggering businesses to increase production to meet this unexpected demand. Such unplanned adjustments can initiate a chain reaction affecting employment, investment, and future consumption patterns in the economy.

Saving Equals Investment

The principle "saving equals investment" is a cornerstone in reaching economic equilibrium. It implies that whatever portion of income is not consumed (i.e., savings) is used to finance investments.
In our model, planned saving is calculated as \(Y - 0.75Y = 0.25Y\). To achieve equilibrium, this planned saving must equal planned investment. By setting \(0.25Y = 40\) and solving, we find \(Y = 160\).
This result verifies equilibrium output through another lens, solidifying the connection between saving and investment as pillars of economic stability. It demonstrates that when savings match investments, the economy operates efficiently without unexpected resource accumulation or depletion.