Problem Set #09: International Trade And Income Taxes In Fairdale Note: In this problem set, we will build on the concepts introduced in the previous problem. If you have not already done so, please complete the previous problem set before you begin this one. When you have completed this Problem Set, you should have a better understanding of the following economic concepts: Complex Multipliers. The Effects of Income Taxes. The Effects of Changes in Net Exports. 1. Introduction Welcome back to Excell Our goal in this problem set is to build on the basic model that we introduced in the previous problem; we will make our macroeconomic model more realistic by allowing the government to use income taxes instead of lump-sum taxes to raise revenues, and by adding an international sector. In this problem set, we will examine the hypothetical economy of Fairdale. Fairdale is small in area, but its population is very large. This makes it a lucrative international trading partner. Other nations of the world buy the few finished manufactured products that Fairdale produces, and in exchange Fairdale trades with the rest of the world for tea, spices, silk, and other products that Fairdale wishes to import. The simplifying assumptions described in the introduction to the previous problem will also hold in this problem set. We will continue to assume that the level of expenditures in Fairdale is the most important factor determining the level of economic activity. All relationships that describe the behavior of agents in Fairdale will be linear. Finally, we will continue to assume that the price level is fixed; all adjustments to changes in the economy are assumed to be real adjustments, rather than inflation. Let's get started! II. Instructions Step 1 - Building The Worksheet You will be building a data base from scratch in this problem set, so bring up a new, empty Excel worksheet. Title it: Problem Set 09: The Economy Of Fairdale Go to cell A4 and type the label: Rincome. Use the Edit and Fill command in cells A5:A165 to enter data on alternative levels of real income for Fairdale, ranging from 0 to 40,000 with a step value of 250. Step 2 - Defining Aggregate Expenditures In Fairdale After gathering extensive information from many people in Fairdale, we found that the behavior of economic agents can be described as follows: In Fairdale, households plan to spend 8250 dollars, even if disposable income is zero. Out of each additional dollar earned, the average household spends 75 cents. The government of Fairdale chooses not to tax households right now. Go to cell B4 and type the label: CON 1. Use the information above to construct a formula for household consumption in cell B5. Copy your formula into the rest of column B for each level of real income. (HINT: Cell B165 should contain the value 38250.) Further, firms in Fairdale plan to invest 6000 dollars, regardless of the level of real national income. The government plans to spend 1000, regardless of the level of real national income; it finances this expenditure by borrowing and hence is running a government budget deficit. Go to cell C4. Type the label INV and use the information above to enter values for investment at each level of real national income. Go to cell D4. Type the label GOV and use the information above to enter values for government spending at each level of real national income. Finally, Fairdale's firms plan to export 5000 dollars worth of goods and services this year regardless of the level of national income. Their imports, however, depend on real national income. If real income is zero, Fairdale will import nothing: for each dollar increase in national income, Fairdale will spend 50 cents on imported goods. Go to cell E4 and type the label: XNET. Use the information above to construct a formula for net exports in cell ES Drag and Paste this formula down column E for each level of real income. (Hint: When real income (Income) is 40000, Fairdale should have a trade deficit of 15,000.) Now you are ready to calculate aggregate expenditures. Go to cell F4 and type the label: C1+I+G+NX. Use the SUM command to calculate aggregate expenditures in cell F5. Copy your formula down column Ffor each level of real income. (Hint: Cell F165 should contain the value 30250.) Good Work! Your last step involves using an IF statement to determine the equilibrium level of real national income. Go to cell G4 and type the label: EQUILI. Use the IF command (introduced in PS#8) to type a formula that will a determine and mark the equilibrium level of real national income in cell GS. Copy your formula into the rest of column G for each level of real income. Take a moment to save your new worksheet as P509. Step 3 - Graphing Your next step is to create an XY (Scatter) graph of the aggregate expenditures curve that you just worked so hard to generate. However, before you do this, you need to create a column of data that will allow you to generate your 45-degree line; remember from the previous problem that you can use this 45-degree line as a marker. Your equilibrium level of real national income occurs where the aggregate expenditures curve crosses the 45-degree line Put a label in column H and add the data that you need. I Create an XY graph of your aggregate expenditures curve and 45 degree line. Title your graph: Equilibrium Level of Real Natl. Income in Fairdale Click on your diagram and then Chart in the top row of your toolbar. Add the investment spending (INV) and government spending (GOV) data to your diagram Carefully compare the information from your worksheet with that from your graph. Do you get the same equilibrium with your diagram and with your IF statement? What is the equilibrium level of real national income? Consider the trade balance at the equilibrium level of real national income. (The trade balance is another way to refer to your net exports column.) What is the trade balance at the equilibrium level of real income? Is it positive or negative? Consider the relationship between the intercept of your aggregate expenditure curve and the equilibrium level of real national income...Can you define your multiplier for Fairdale? is it a "simple multiplier"? Be ready to answer these questions when you do the quiz that accompanies this problem. Step 4 - Income Taxes In Fairdale Suppose that the government of Fairdale would like to raise revenues so that it can pay for its expenditures rather than running a deficit. Suppose further that they are considering a 20-percent income tax on households; that is, households would have to send 20 cents to the government for each additional dollar that they earn. Go to cell 14 and type the label: CON 2. Use the information above to construct a formula for your new consumption function in cell 15. Copy this formula into column I for each level of real income. (Hint: Your final value for CON2, in cell 1165, should be 32250.) Compare this new consumption function with your old one. What has happened to autonomous consumption? What has happened to consumption at every other level of real national income? Go to cell 34 and type the label: C2+I+G+NX. Use the SUM command to construct a formula for your new aggregate expenditure function in cell J5. (Note: The columns that you need to sum are no longer adjacent to one another, so you may have to slightly modify the format of your SUM command.) I Copy your formula into the rest of columns for each level of real income (Hint: Cell J165 should contain the value 24250.) Go to cell K4 and type the label: EQUIL 2 Beginning in cell K5, use the IF command to type a formula that will determine and mark the equilibrium level of real national income Copy this formula into the rest of column K for each level of real income. Add your new aggregate expenditure function to your graph. Carefully compare your new and old aggregate expenditure functions. What has happened to the equilibrium level of real income? What has happened to the overall level of economic activity? What are the pros and the cons of this sort of taxation for government? What has happened to your multiplier? Calculate it again. Why does it make sense that the multiplier will be smaller when the government places an income tax on households? Be ready for these quiz questions! Step 5 - Increasing Exports Suppose that the government of Fairdale is considering a policy that would encourage a more positive trade balance for Fairdale. They initiate policy that increases exports to 6,550. At the same time, they place tariffs on markets to discourage consumption of imports; the goal is to decrease the fraction of each marginal dollar spent on imports from .5 to.4. They hire you as a consultant to help them determine the impact of this set of policies. Go to cell L4 and type the label: XNET2. Construct a formula for your new net exports in cell L5. (You may want to Copy your first net export formula from cell Es. Then, use the Edit key (F2) to modify it. Make certain that your formula indicates that imports are 40 percent of real income, which is found in column A.) Copy your formula into column L for each level of real income. (Hint: Cell L165 should contain the value - 9450.) Go to cell M4 and type the label: C2+I+G+NX2 Use the SUM command to construct a formula for your new aggregate expenditure function in cell M5. Copy this formula into column M for each level of real income. (Hint: Cell M165 should contain the value 29800.) Add your new aggregate expenditures curve to your diagram. Go to cell N4 and type the label: EQUIL 3. In cell N5, use the IF command to type a formula that will determine and mark the equilibrium level of real national income. Copy your formula into the rest of column N. What can you say about the effects of increased exports and decreased imports on the economy of Fairdale? Given the information that you have available about Fairdale would you recommend this policy to the government? Carefully consider the answers to these questions. Step 6 - Completing Your Work Only if you need to print a copy of your worksheet. You will need to use condensed printing, since your worksheet is too wide for a standard page. Then move on to complete the quiz and other assignments related to this worksheet and graphs. Make sure that you save your work before you leave your computer. See you next time! Problem Set #09: International Trade And Income Taxes In Fairdale Note: In this problem set, we will build on the concepts introduced in the previous problem. If you have not already done so, please complete the previous problem set before you begin this one. When you have completed this Problem Set, you should have a better understanding of the following economic concepts: Complex Multipliers. The Effects of Income Taxes. The Effects of Changes in Net Exports. 1. Introduction Welcome back to Excell Our goal in this problem set is to build on the basic model that we introduced in the previous problem; we will make our macroeconomic model more realistic by allowing the government to use income taxes instead of lump-sum taxes to raise revenues, and by adding an international sector. In this problem set, we will examine the hypothetical economy of Fairdale. Fairdale is small in area, but its population is very large. This makes it a lucrative international trading partner. Other nations of the world buy the few finished manufactured products that Fairdale produces, and in exchange Fairdale trades with the rest of the world for tea, spices, silk, and other products that Fairdale wishes to import. The simplifying assumptions described in the introduction to the previous problem will also hold in this problem set. We will continue to assume that the level of expenditures in Fairdale is the most important factor determining the level of economic activity. All relationships that describe the behavior of agents in Fairdale will be linear. Finally, we will continue to assume that the price level is fixed; all adjustments to changes in the economy are assumed to be real adjustments, rather than inflation. Let's get started! II. Instructions Step 1 - Building The Worksheet You will be building a data base from scratch in this problem set, so bring up a new, empty Excel worksheet. Title it: Problem Set 09: The Economy Of Fairdale Go to cell A4 and type the label: Rincome. Use the Edit and Fill command in cells A5:A165 to enter data on alternative levels of real income for Fairdale, ranging from 0 to 40,000 with a step value of 250. Step 2 - Defining Aggregate Expenditures In Fairdale After gathering extensive information from many people in Fairdale, we found that the behavior of economic agents can be described as follows: In Fairdale, households plan to spend 8250 dollars, even if disposable income is zero. Out of each additional dollar earned, the average household spends 75 cents. The government of Fairdale chooses not to tax households right now. Go to cell B4 and type the label: CON 1. Use the information above to construct a formula for household consumption in cell B5. Copy your formula into the rest of column B for each level of real income. (HINT: Cell B165 should contain the value 38250.) Further, firms in Fairdale plan to invest 6000 dollars, regardless of the level of real national income. The government plans to spend 1000, regardless of the level of real national income; it finances this expenditure by borrowing and hence is running a government budget deficit. Go to cell C4. Type the label INV and use the information above to enter values for investment at each level of real national income. Go to cell D4. Type the label GOV and use the information above to enter values for government spending at each level of real national income. Finally, Fairdale's firms plan to export 5000 dollars worth of goods and services this year regardless of the level of national income. Their imports, however, depend on real national income. If real income is zero, Fairdale will import nothing: for each dollar increase in national income, Fairdale will spend 50 cents on imported goods. Go to cell E4 and type the label: XNET. Use the information above to construct a formula for net exports in cell ES Drag and Paste this formula down column E for each level of real income. (Hint: When real income (Income) is 40000, Fairdale should have a trade deficit of 15,000.) Now you are ready to calculate aggregate expenditures. Go to cell F4 and type the label: C1+I+G+NX. Use the SUM command to calculate aggregate expenditures in cell F5. Copy your formula down column Ffor each level of real income. (Hint: Cell F165 should contain the value 30250.) Good Work! Your last step involves using an IF statement to determine the equilibrium level of real national income. Go to cell G4 and type the label: EQUILI. Use the IF command (introduced in PS#8) to type a formula that will a determine and mark the equilibrium level of real national income in cell GS. Copy your formula into the rest of column G for each level of real income. Take a moment to save your new worksheet as P509. Step 3 - Graphing Your next step is to create an XY (Scatter) graph of the aggregate expenditures curve that you just worked so hard to generate. However, before you do this, you need to create a column of data that will allow you to generate your 45-degree line; remember from the previous problem that you can use this 45-degree line as a marker. Your equilibrium level of real national income occurs where the aggregate expenditures curve crosses the 45-degree line Put a label in column H and add the data that you need. I Create an XY graph of your aggregate expenditures curve and 45 degree line. Title your graph: Equilibrium Level of Real Natl. Income in Fairdale Click on your diagram and then Chart in the top row of your toolbar. Add the investment spending (INV) and government spending (GOV) data to your diagram Carefully compare the information from your worksheet with that from your graph. Do you get the same equilibrium with your diagram and with your IF statement? What is the equilibrium level of real national income? Consider the trade balance at the equilibrium level of real national income. (The trade balance is another way to refer to your net exports column.) What is the trade balance at the equilibrium level of real income? Is it positive or negative? Consider the relationship between the intercept of your aggregate expenditure curve and the equilibrium level of real national income...Can you define your multiplier for Fairdale? is it a "simple multiplier"? Be ready to answer these questions when you do the quiz that accompanies this problem. Step 4 - Income Taxes In Fairdale Suppose that the government of Fairdale would like to raise revenues so that it can pay for its expenditures rather than running a deficit. Suppose further that they are considering a 20-percent income tax on households; that is, households would have to send 20 cents to the government for each additional dollar that they earn. Go to cell 14 and type the label: CON 2. Use the information above to construct a formula for your new consumption function in cell 15. Copy this formula into column I for each level of real income. (Hint: Your final value for CON2, in cell 1165, should be 32250.) Compare this new consumption function with your old one. What has happened to autonomous consumption? What has happened to consumption at every other level of real national income? Go to cell 34 and type the label: C2+I+G+NX. Use the SUM command to construct a formula for your new aggregate expenditure function in cell J5. (Note: The columns that you need to sum are no longer adjacent to one another, so you may have to slightly modify the format of your SUM command.) I Copy your formula into the rest of columns for each level of real income (Hint: Cell J165 should contain the value 24250.) Go to cell K4 and type the label: EQUIL 2 Beginning in cell K5, use the IF command to type a formula that will determine and mark the equilibrium level of real national income Copy this formula into the rest of column K for each level of real income. Add your new aggregate expenditure function to your graph. Carefully compare your new and old aggregate expenditure functions. What has happened to the equilibrium level of real income? What has happened to the overall level of economic activity? What are the pros and the cons of this sort of taxation for government? What has happened to your multiplier? Calculate it again. Why does it make sense that the multiplier will be smaller when the government places an income tax on households? Be ready for these quiz questions! Step 5 - Increasing Exports Suppose that the government of Fairdale is considering a policy that would encourage a more positive trade balance for Fairdale. They initiate policy that increases exports to 6,550. At the same time, they place tariffs on markets to discourage consumption of imports; the goal is to decrease the fraction of each marginal dollar spent on imports from .5 to.4. They hire you as a consultant to help them determine the impact of this set of policies. Go to cell L4 and type the label: XNET2. Construct a formula for your new net exports in cell L5. (You may want to Copy your first net export formula from cell Es. Then, use the Edit key (F2) to modify it. Make certain that your formula indicates that imports are 40 percent of real income, which is found in column A.) Copy your formula into column L for each level of real income. (Hint: Cell L165 should contain the value - 9450.) Go to cell M4 and type the label: C2+I+G+NX2 Use the SUM command to construct a formula for your new aggregate expenditure function in cell M5. Copy this formula into column M for each level of real income. (Hint: Cell M165 should contain the value 29800.) Add your new aggregate expenditures curve to your diagram. Go to cell N4 and type the label: EQUIL 3. In cell N5, use the IF command to type a formula that will determine and mark the equilibrium level of real national income. Copy your formula into the rest of column N. What can you say about the effects of increased exports and decreased imports on the economy of Fairdale? Given the information that you have available about Fairdale would you recommend this policy to the government? Carefully consider the answers to these questions. Step 6 - Completing Your Work Only if you need to print a copy of your worksheet. You will need to use condensed printing, since your worksheet is too wide for a standard page. Then move on to complete the quiz and other assignments related to this worksheet and graphs. Make sure that you save your work before you leave your computer. See you next time