In an economy with no government and no foreign sectors, autonomous consumer spending is \(\$ 250\) billion, planned investment spending is \(\$ 350\) billion, and the marginal propensity to consume is \(2 / 3\). a. Plot the aggregate consumption function and planned aggregate spending. b. What is unplanned inventory investment when real GDP equals \(\$ 600\) billion? c. What is \(Y^{*}\), income-expenditure equilibrium GDP? d. What is the value of the multiplier? e. If planned investment spending rises to \(\$ 450\) billion, what will be the new \(Y^{*}\) ?

Short Answer

Expert verified
In summary, we were able to find the consumption function, calculate planned aggregate spending, calculate unplanned inventory investment, find the income-expenditure equilibrium GDP, and the multiplier. The consumption function is given by \(C = \$250 + (2/3)Y\). The planned aggregate spending is \(PAS = \$600 + (2/3)Y\). The unplanned inventory investment is -\$400 billion. The income-expenditure equilibrium GDP (\(Y^*\)) is \$1800 billion, and the multiplier is 3. If investment spending increases to \$450 billion, the new equilibrium GDP (\(Y^{*'}\)) is \$2700 billion.

Step by step solution

01

Identify the Consumption Function Formula

The Consumption Function (C) is given by the formula: \(C = C_0 + MPC \cdot Y\), where \(C_0\) is autonomous consumer spending, MPC is the marginal propensity to consume, and Y is the real GDP. Step 2: Find the Consumption Function (C)
02

Plug in the Given Values

Using the given values for autonomous consumer spending (\(C_0 = \$250\) billion), planned investment spending (\(350\) billion), and the marginal propensity to consume (MPC = \(2 / 3\)), we can find the consumption function (C): \(C = \$250 + (2/3)Y\). Step 3: Plot the Aggregate Consumption Function (C)
03

Draw the Consumption Function Graph

To draw the aggregate consumption function (C) graph, plot the consumption function (\(C = \$250 + (2/3)Y\)) on the vertical axis against real GDP (Y) on the horizontal axis. Step 4: Find Planned Aggregate Spending (PAS)
04

Identify Planned Aggregate Spending Formula

Planned Aggregate Spending (PAS) is the sum of the consumption function and planned investment spending: \(PAS = C + I\), where I is planned investment spending. Step 5: Calculate Planned Aggregate Spending (PAS)
05

Plug in the Given Values

Using the consumption function identified in Step 2 and the given planned investment spending value (\(I = \$350\) billion), we can calculate Planned Aggregate Spending (PAS): \(PAS = (\$250 + (2/3)Y) + \$350 = \$600 + (2/3)Y\). Step 6: Plot Planned Aggregate Spending (PAS)
06

Draw the PAS Graph

To draw the planned aggregate spending (PAS) graph, plot the planned aggregate spending function (\(PAS = \$600 + (2/3)Y\)) on the vertical axis against real GDP (Y) on the horizontal axis. Step 7: Unplanned Inventory Investment
07

Identify Unplanned Inventory Investment Formula

Unplanned inventory investment occurs when there is a difference between the actual GDP (Y) and Planned Aggregate Spending (PAS), and it can be found using the formula: Unplanned inventory investment = GDP - PAS. Step 8: Calculate Unplanned Inventory Investment
08

Plug in the Given Values

Given that the real GDP = \(\$600\) billion, we can now find the unplanned inventory investment using the formula: Unplanned inventory investment = \(\$600\) - PAS. PAS = \(\$600 + (2/3)(\$600)\). Unplanned inventory investment = \(\$600 - (\$600 + (2/3)(\$600)) = -\$400\) billion. Step 9: Income-Expenditure Equilibrium GDP (\(Y^*\))
09

Find Equilibrium Condition

At income-expenditure equilibrium, the total spending (C+I) equals the total output (Y): \(Y^* = C + I\). Step 10: Calculate \(Y^*\)
10

Solve for Equilibrium GDP

Using the equilibrium condition and the consumption function and investment spending, we can find \(Y^*\): \(Y^* = \$250 + (2/3)Y^* + \$350\). Solve for \(Y^*\) to get \(Y^* = \$1800\). Step 11: Find the Multiplier
11

Identify the Multiplier Formula

The multiplier is given by the formula: Multiplier = \(\frac{1}{1 - MPC}\). Step 12: Calculate the Multiplier
12

Plug in the Given Values

Using the given marginal propensity to consume (MPC = \(2 / 3\)), we can find the multiplier: Multiplier = \(\frac{1}{1 - (2/3)} = 3\). Step 13: New \(Y^*\) If Investment Spending Increases
13

Adjust for New Investment Spending

Given the new planned investment spending (\(I = \$450\) billion), we can calculate the new income-expenditure equilibrium GDP (\(Y^{*'}\)): \(Y^{*'} = C + I' = \$250 + (2/3)Y^{*'} + \$450\). Solve for \(Y^{*'}\) to get \(_{*'} = \$2700\).

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Most popular questions from this chapter

An economy has a marginal propensity to consume of \(0.5,\) and \(Y^{*},\) income- expenditure equilibrium GDP, equals \(\$ 500\) billion. Given an autonomous increase in planned investment of \(\$ 10\) billion, show the rounds of increased spending that take place by completing the accompanying table. The first and second rows are filled in for you. In the first row, the increase of planned investment spending of \(\$ 10\) billion raises real GDP and \(Y D\) by \(\$ 10\) billion, leading to an increase in consumer spending of \(\$ 5\) billion \((M P C \times\) change in disposable income) in row \(2,\) raising real GDP and \(Y D\) by a further \(\$ 5\) billion. a. What is the total change in real GDP after the 10 rounds? What is the value of the multiplier? What would you expect the total change in \(Y^{*}\) to be based on the multiplier formula? How do your answers to the first and third questions compare? b. Redo the table starting from round 2 , assuming the marginal propensity to consume is \(0.75 .\) What is the total change in real GDP after 10 rounds? What is the value of the multiplier? As the marginal propensity to consume increases, what happens to the value of the multiplier?

The Bureau of Economic Analysis reported that, in real terms, overall consumer spending increased by \(\$ 66.2\) billion during the second quarter of \(2014 .\) a. If the marginal propensity to consume is \(0.52,\) by how much will real GDP change in response? b. If there are no other changes to autonomous spending other than the increase in consumer spending in part a, and unplanned inventory investment, \(I_{\text {Unplanned }}\), decreased by \(\$ 50\) billion, what is the change in real GDP? c. GDP at the end of the first quarter in 2014 was \(\$ 16,014.1\) billion. If GDP were to increase by the amount calculated in part b, what would be the percent increase in GDP?

How will planned investment spending change as the following events occur? a. The interest rate falls as a result of Federal Reserve policy. b. The U.S. Environmental Protection Agency decrees that corporations must upgrade or replace their machinery in order to reduce their emissions of sulfur dioxide. c. Baby boomers begin to retire in large numbers and reduce their savings, resulting in higher interest rates.

Assuming that the aggregate price level is constant, the interest rate is fixed, and there are no taxes and no foreign trade, what will be the change in GDP if the following events occur? a. There is an autonomous increase in consumer spending of \(\$ 25\) billion; the marginal propensity to consume is \(2 / 3\). b. Firms reduce investment spending by \(\$ 40\) billion; the marginal propensity to consume is 0.8 . c. The government increases its purchases of military equipment by \(\$ 60\) billion; the marginal propensity to consume is 0.6

The U.S. economy slowed significantly in early 2008 , and policy makers were extremely concerned about growth. To boost the economy, Congress passed several relief packages (the Economic Stimulus Act of 2008 and the American Recovery and Reinvestment Act of 2009) that combined would deliver about \(\$ 700\) billion in government spending. Assume, for the sake of argument, that this spending was in the form of payments made directly to consumers. The objective was to boost the economy by increasing the disposable income of American consumers. a. Calculate the initial change in aggregate consumer spending as a consequence of this policy measure if the marginal propensity to consume $(M P C)\( in the United States is \)0.5 .$ Then calculate the resulting change in real GDP arising from the \(\$ 700\) billion in payments. b. Illustrate the effect on real GDP with the use of a graph depicting the income-expenditure equilibrium. Label the vertical axis "Planned aggregate spending, \(A E_{\text {Planned }}\) " and the horizontal axis "Real GDP." Draw two planned aggregate expenditure curves $\left(A E_{\text {Planned } 1}\right.\( and \)A E_{\text {Planned } 2}$ ) and a 45 -degree line to show the effect of the autonomous policy change on the equilibrium.

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