HW07_IS_a.doc Foundations of Economic Analysis Stratton
Homework #7 Name ______
Objective: to provide practice and assessment of your understanding of the determinants of Aggregate Expenditures and equilibrium conditions in the “real goods markets” in the U.S. Your ability to demonstrate understanding, insight and/or the ability to use the material is the primary purpose of the assessment. Thus full credit will only be earned if you follow the directions carefully and provide the explanation, description, and thought process as directed. Each numbered question is worth 2 points – total 50 points.
Instructions: In your own words explain the key differences for each pair of terms, in the space provided or attach additional sheets if necessary.
Terms:
1. Aggregate expenditures and real GDP – AE is the sum of planned expenditures while GDP is the sum of actual expenditures of the four major sectors (actors): C + I + G + X – M.
2. Autonomous and (Income) Induced Expenditures – Autonomous expenditures are planned spending which are independent of the level of (national income). Induced expenditures are planned spending that vary in response to changes in the level of (national) income.
3. Focus of short-run economic policy and the focus of long-run economic policy – Long-run economic policies tend to focus on determinants of economic growth and potential GDP. Short-run economic policies tend to focus on managing aggregate expenditures to reduce fluctuations around the potential GDP. It focuses on the goals of full employment and low inflation.
4. Relative prices and absolute price level – Relative prices compare the price of one option (good) to another and impact our decisions between substitutes. The absolute price level measures the overall relationship between prices in general and the value of the currency. An example of an increase in the absolute price level would be a doubling of all prices. Note in such a case no relative prices are changed. In reality, changes in the absolute price level are accompanied by relative price changes, since not all prices will increase at the same rate.
5. Actual and equilibrium GDP – Actual GDP is the level of GDP observed. Equilibrium GDP is the level of GDP at which planned spending is equal to actual spending.
Short Answer Questions: Answer each question, indicating any assumptions you make, explaining your thinking, and showing all work where appropriate.
6. Explain the impact an increase in wealth is expected to have on planned consumption.
Wealth is expected to be positively related with planned consumption. Households can consume out of their wealth, so as wealth increases (holding other factors constant) households have more resources from which to consume. Additionally, households with greater wealth have more of an economic cushion and do not need to save as much out of their current income.
7. Explain the impact an increase in personal income taxes is expected to have on planned consumption.
Planned consumption is expected to be negatively (inversely) related to personal taxes. Households consume out of disposable income. Disposable income equals gross income (personal income in the NIPA) minus personal taxes. Thus an increase in personal taxes (holding other factors constant) will reduce disposable income. Since planned consumption is positively related to personal disposable income, the increased tax will reduce disposable income and thus planned consumption.
8. Your text indicates that unplanned inventory changes are one mechanism through which an economy adjust toward equilibrium. Assume the current GDP is greater than planned expenditures. Explain how the economy adjusts toward equilibrium through adjustments in inventories.
If Y > AE [or leakages > injections] total sales will be less than expected (or planned) and inventories will increase more than planned (desired). If inventories are greater than desired, firms will tend to reduce production to reduce unplanned inventories. Therefore, actual spending will decrease toward the equilibrium level of GDP.
9. Explain the impact an increase in real interest rates is expected to have on planned investment (gross private domestic investment).
The real interest rate represents the opportunity cost of using funds. Thus, the higher the opportunity cost (real interest rates) the fewer profitable investment projects exist. Thus, businesses will plan to invest less at higher interest rates.
10. The text indicates that planned imports depend on the level of real domestic income (personal disposable income). Explain the impact an increase in real domestic income is expected to have on planned imports.
Household planned spending on imports is similar to household planned spending on consumption. That is households plan to purchase goods and services, some of which are from foreign suppliers. Thus, as real domestic income increases, planned consumption is expected to also increase (as long as foreign goods are not all inferior goods). However, not all of the increased income will be devoted to increases in the purchase of imports, thus the increase in imports will be less than the increase in real income.
Scenario 1: In Akropolis there is no inflation (prices are constant), the government budget is balanced and net tax revenue is collect as a head tax (each adult in the economy pays a flat dollar amount equal to government expenditures divided by the number of adults). The table below depicts the data for Akropolis. In this table, GDP is the actual real GDP, C is planned consumption, I is planned investment, G is planned government spending, X is revenue from exports, M is planned import expenditure, and NT is net tax revenue. Use these data to answer the questions below. Be sure to answer the questions as completely as you can and to show your work!
All data are in millions of constant dollars.
GDP / C / I / G / X / M / NT / AE8000 / 5175 / 2000 / 1100 / 1500 / 1400 / 1100 / 8375
8500 / 5550 / 2000 / 1100 / 1500 / 1400 / 1100 / 8750
9000 / 5925 / 2000 / 1100 / 1500 / 1400 / 1100 / 9125
9500 / 6300 / 2000 / 1100 / 1500 / 1400 / 1100 / 9500
10000 / 6675 / 2000 / 1100 / 1500 / 1400 / 1100 / 9875
10500 / 7050 / 2000 / 1100 / 1500 / 1400 / 1100 / 10250
11000 / 7425 / 2000 / 1100 / 1500 / 1400 / 1100 / 10625
11500 / 7800 / 2000 / 1100 / 1500 / 1400 / 1100 / 11000
12000 / 8175 / 2000 / 1100 / 1500 / 1400 / 1100 / 11375
12500 / 8550 / 2000 / 1100 / 1500 / 1400 / 1100 / 11750
13000 / 8925 / 2000 / 1100 / 1500 / 1400 / 1100 / 12125
11. The MPC is the proportion of each additional dollar of real GDP that households plan to consume (change in planned consumption / change in real GDP). What is the MPC in Akropolis?
Change in real GDP of $500 million changes planned C by $375 million. Thus MPC = 0.75. Or households plan to consume 75 percent of each additional dollar of income.
12. What proportion of each additional dollar of real GDP do households plan to save?
If households plan to consume 75 percent of each additional dollar of income and there are no additional taxes that must be paid, then they must plan to save 25 percent.
13. What is the equilibrium level of real GDP in Akropolis?
Equilibrium is when actual real GDP equals planned levels of spending, or real GDP = C + I + G + (X – M). This occurs at $9500 million.
14. Calculate the total leakages and total injections at an actual GDP of $10 trillion ($10,000 million on the table).
Leakages = S + T + M = 2225 + 1100 + 1400 = 4725
Injections = I + G + X = 2000 + 1100 + 1500 = 4600
15. If interest rates increased in Akropolis such that planned investment decreased to $1800 million, what would be the new equilibrium level of real GDP?
The investment multiplier in Akropolis is [1 / (1- 0.75)] = [1 / 0.25] = 4. If planned investment decreases to $1800 million, this is a decline of $200 million. The new equilibrium level of real GDP is $9500 million - $800 million or $8700 million.
16. If Akropolis increases government spending to $1,600 million what will be the new equilibrium level of real GDP? (Remember, Akropolis always has a balanced budget! Use the original data; ignore the interest rate change the last question.)
The government spending multiplier in Akropolis is [1 / (1 - 0.75)] = [1 / 0.25] = 3. If government spending increases by $500 million and NT were constant then, the new equilibrium level of real GDP is $9500 million + $2000 million or $11,500 million.
However, NT also increases by $500 million. So households will have $500 million less disposable income. If they to plan to reduce consumption by 75 percent of each dollar lost, this will reduce planned consumption by $375 million. So government spending increases by $500 million and consumption decreases by $375 million. The net change is $125 million. The new equilibrium level of real GDP is $9500 million + $500 million or $10,000 million. (125 * 4).
Scenario 2: In Cantonese there is no inflation (prices are constant), the government budget is balanced and net tax revenue is collect as a head tax (each adult in the economy pays a flat dollar amount equal to government expenditures divided by the number of adults). The equations below depict the economic structure of Cantonese. All data are in millions of constant dollars.
C = 240 + 0.8 (Y – TP)
I = I0 = 500
G = G0 = 300
X = X0 = 300
M = M0 = 400
In these equations, Y is the actual real GDP, C is planned consumption, I is planned investment, G is planned government spending, X is revenue from exports, and M is planned import expenditure. Use these data to answer the questions below. Be sure to answer the questions as completely as you can and to show your work!
17. The MPC is the proportion of each additional dollar of real GDP that households plan to consume (change in planned consumption / change in real GDP). What is the MPC in Cantonese?
The MPC is the coefficient of the consumption function – 0.80. Thus a change in real GDP of $500 million changes planned C by $400 million.
18. What is the equilibrium level of real GDP in Cantonese?
Equilibrium is when actual real GDP equals planned levels of spending (AE), or real GDP = C + I + G + (X – M). In this example: since there is a balanced budget, TP = G0 = 300.
Y = 240 + 0.8 (Y – 300) + 500 + 300 + (300 – 400)
Y – 0.8 Y = 240 – 240 + 500 + 300 – 100
Y = (1/0.2) (700) = 5(700) = $3500. Equilibrium GDP is $3500 million.
19. Calculate the total leakages and total injections at an actual GDP of $5 trillion.
S = Y - TP – C = 5000 – 300 – 4000 = 700
Leakages = S + T + M = 700 + 300 + 400 = 1400
Injections = I + G + X = 500 + 300 + 300 = 1100
20. If interest rates decreased in Cantonese such that planned investment decreased to $600 million, what would be the new equilibrium level of real GDP?
The investment multiplier in Cantonese is [1 / (1- 0.8)] = [1 / 0.2] = 5. If planned investment increases to $600 million, this is an increase of $100 million. The new equilibrium level of real GDP is $3500 million + $500 million or $4000 million.
21. If Cantonese increases government spending to $400 million what will be the new equilibrium level of real GDP? (Remember, Cantonese always has a balanced budget! Use the original data; ignore the interest rate change the last question.)
The government spending multiplier in Cantonese is [1 / (1 - 0.8)] = [1 / 0.2] = 5. If government spending increases by $100 million and NT were constant then, the new equilibrium level of real GDP is $3500 million + $500 million or $4,000 million.
However, NT also increases by $100 million. So households will have $100 million less disposable income. If they to plan to reduce consumption by 80 percent of each dollar lost, this will reduce planned consumption by $80 million. So government spending increases by $100 million and consumption decreases by $80 million. The net change is $20 million. The new equilibrium level of real GDP is $3500 million + $100 million or $3,600 million. (20 * 5).
Scenario 3: The concept of elasticity measure how responsive one variable is to changes in another. We can define the interest rate elasticity of investment as the ratio of the % change in I caused by the % change in interest rates [%D I / %D r]. We can define the interest rate elasticity of actual real income (GDP) as the ratio of the % change in Y caused by the % change in interest rates [%D Y / %D r]. Assume the current equilibrium real income is $10 trillion and the equilibrium interest rate is 4%. (This is one point on the IS curve.) Explain the impact on the IS curve and the interest rate elasticity of actual real income of each of the following changes.
22. The marginal propensity to consume increases.
An increase in the MPC means that the spending multiplier will be greater. Thus, an autonomous change in AE will cause a larger change in equilibrium GDP. [The multiplier is greater.] Thus the slope of the IS curve will be flatter and the interest rate elasticity of actual real income will increase. The same change in r will lead to a greater change in Y.
23. A decrease in the interest rate elasticity of investment.
A decrease in the interest rate elasticity of investment means that a given change in r will lead to a smaller change in I. Thus the slope of the investment demand function (IRE) and the IS curve will be steeper. The interest rate elasticity of actual real income will decrease (become less elastic). The same change in r will lead to a smaller change in Y.