Consider an economy described by the following equations: $$\begin{array}{l}Y=C+I+G \\\C=100+0.75(Y-T) \\\I=500-50 r \\\G=125 \\\T=100\end{array}$$ where \(Y\) is \(G D P, C\) is consumption, \(I\) is investment, \(G\) is government purchases, \(T\) is taxes, and \(r\) is the interest rate. If the economy were at full employment (that is, at its natural level of output). GDP would be 2,000. a. Explain the meaning of each of these equations. b. What is the marginal propensity to consume in this economy? c. Suppose the central bank adjusts the money supply to maintain the interest rate at 4 percent, so \(r=4 .\) Solve for GDP. How does it compare to the full- employment level? d. Assuming no change in monetary policy, what change in government purchases would restore full employment? e. Assuming no change in fiscal policy, what change in the interest rate would restore full employment?

Step by step solution

01

- Understanding the Equations

Understand each equation in the context of the economy: The first equation, Y=C+I+G, represents the composition of GDP, which sums up Consumption (C), Investment (I), and Government Purchases (G). The second equation, C=100 + 0.75(Y-T), indicates how Consumption (C) is dependent on disposable income, which is output (Y) minus taxes (T). The coefficient 0.75 is the marginal propensity to consume, and 100 is the autonomous consumption that does not depend on income. The third equation, I = 500 - 50r, shows that Investment (I) is inversely related to the interest rate (r); this is because higher interest rates generally lead to lower investment levels. The fourth equation simply states that Government Purchases (G) are 125 and Taxes (T) are 100.

02

- Marginal Propensity to Consume

Identify the marginal propensity to consume (MPC) directly from the consumption function. The MPC is the coefficient of (Y-T) in the consumption equation, which represents the change in consumption for a change in disposable income. The MPC in this economy is 0.75.

03

- Solving for GDP when r=4%

Solve for GDP (Y) when the interest rate (r) is fixed at 4%: First, substitute the value of the interest rate into the investment equation to find I = 500 - 50(4) and calculate I. Then, substitute the value of I, G, and T into the GDP equation to solve for Y.

04

- Comparing GDP to Full-Employment Level

Compare the GDP found in the previous step to the full-employment GDP (2,000). This will show if the economy at an interest rate of 4% is over or under the full-employment level.

05

- Fiscal Policy to Restore Full Employment

Calculate the change in government purchases (ΔG) needed to achieve full employment GDP (Y = 2,000). Assume no change in monetary policy means keep interest rate (r) fixed as previously calculated. Set the total spending equal to 2,000 and solve for the change in G.

06

- Monetary Policy to Restore Full Employment

Calculate the change in interest rate (Δr) that would restore full employment. Set the GDP equation equal to 2,000 and use the investment equation to express I in terms of r, then solve for the new interest rate needed to achieve full employment GDP.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

GDP Composition

In macroeconomics, the GDP or Gross Domestic Product represents the total value of all goods and services produced over a specific period within a country. It's essentially the size of the economy. GDP composition is broken down into three main components:

• Consumption (C): This includes all private spending on final goods and services.
• Investment (I): This covers business expenditures on capital and residential constructions, as well as changes in business inventories.
• Government Purchases (G): This is the total government spending on final goods and services.

The equation Y = C + I + G shows us how these components add up to the total GDP. Understanding the composition helps in analyzing how changes in each sector can affect overall economic performance.

Marginal Propensity to Consume

The concept of Marginal Propensity to Consume (MPC) is vital to understanding consumer behavior in relation to income changes. It tells us what fraction of additional income will be spent on consumption. For instance, an MPC of 0.75 means if consumers receive an extra dollar, 75 cents of that dollar will be used to purchase goods and services, and the remaining 25 cents will be saved.

The MPC is derived from the consumption function, which can be represented as C = a + b(Y-T), where a is autonomous consumption, b is the MPC, Y is income, and T is taxes. In our economy's context, the MPC is 0.75, which signifies a high tendency to consume out of additional income and reflects a positive relationship between disposable income and consumption.

Fiscal Policy

Fiscal policy involves the use of government spending and taxation to influence the economy. When an economy is not at full employment, government can utilize fiscal tools to adjust the level of GDP. There are two main levers:

• Government Spending (G): An increase in government purchases can directly raise aggregate demand and GDP.
• Taxes (T): Adjusting taxation indirectly influences consumption by altering disposable income.

For example, to restore full employment, the government might increase public expenditures on infrastructure. This would increase overall demand and should help push the economy towards its full employment GDP.

Monetary Policy

Monetary policy involves the management of the money supply and interest rates, and is primarily conducted by a country's central bank. The policy's main goal is to achieve full employment, stable prices, and moderate long-term interest rates. Changes in the interest rate influence investment; as rates decrease, investment generally increases because the cost of borrowing is lower.

Using the exercise as a reference, if the central bank sets the interest rate at 4 percent, it is using monetary policy to control economic activity. Should the economy not be at full employment, the central bank could lower interest rates to encourage investment and spend more, moving the economy toward full employment.

Full Employment

Full employment is a situation where all available labor resources are being used in the most economically efficient way. It does not imply zero unemployment, as there will always be some frictional and structural unemployment, but it does suggest that cyclical unemployment is nonexistent.

When an economy is at full employment, it produces at its natural level of output, also referred to as potential GDP. In the exercise, full employment GDP is 2,000. Any deviation from this level would indicate an economy that is either over-performing (overheating) or underperforming (recessionary), with corresponding policy implications for restoring equilibrium.