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ill) I Dutput, business cycles, growth ti employment EXERCISES Foa CHAPTER 5 Eureka 5.1 Suppose we have the following information for an economy: {a} Plot the AD and AS curves in a carefully labeled diagram. {b} What are the short-run equilibrium values of real GDP and the price level? Exercise 5.2 Suppose we learn that potential output is Slit] for the economy in Exercise 5.1. {a} Add a line to your diagram for Exemise ii to illustrate potential GDP. {b} What is the size of any output gap you see in the diagram? Eureka 5.? Potential GDP is determined by the size of the labour force, the stock of capital and the state of technology used in the production process. Assume the labour force grows over time, and research and development lead to improvements in technology, and productivity. Use an ADEAS diagram to illustrate potential GDP both before and after the growth in labour force and the improvement in technology. Eureka 5.4 Growth in potential output is determined by growth in the labour force and growth in labour productivity. Suppose the labour force grows by 1.5 percent a year and labour productivity, based on increased capital and improved technology, grows by 1.11] percent a year. {a} What is the annual growth in potential output? {h} Illustrate the growth in potential output in an ADIAS diagram. {c} Aggregate demand is not changed by the change in potential output. Indicate any output gap caused by the change in potential outpuL Exercise 5.5 Suppose we have the following data for an economy: Exercises for Chapter 5 I 121 Year Potential output Real GDP Calculate the output gap for each year in this economy. Plot the output gap in a time series diagram. Date the timing of the phases of any business cycles you see in your plot of the output gap. Exercise 5.6 Draw an ADIAS diagram that shows an economy called Westland in short-run equi- librium with GDP equal to potential GDP. {a} Suppose a slowdown in the rate of growth of GDP in China cuts Chinese imports of primary prcducm from Westland. Using your ADIAS diagram illustrate and explain your forecast for the effects of this change on the equilibrium GDP and price level in Westland. {b} What effect1 if any, would a slowdown in GDP growth in China have on employment and unemployment rates in Westland? Explain why. Exercise 5.? Optional: Consider an economy described by the following: AD: 1' = 2250' 10F, AS:F=I25+U.1Y. {a} What are the short-mn equilibrium values for real GDP and the price level? {h} Assume potential output is son and draw an ADIASJFP diagram to show the initial short-run equilibrium real GDP1 price level and potential output. to} Changes in international market conditions drive up prices for crude oil and base metals. Increased production costs driven by these higher input prices raise the general price level by 5 at every level of outpuL Write the equation of the new AS curve. What are the new short-11m equilibrium real GDP and price level? {d} Draw the new AS curve in your diagram for {b}. What is the size of the output gap? Exercise 6.1 Suppose that in an economy with no government the aggregate expenditure function is: AE = 50+0.75Y. (a) Draw a diagram showing the aggregate expenditure function, and indicate the level of planned expenditure when income is 150. (b) In this same diagram, show what would happen to aggregate expenditure if income increased to 200. (c) What are the levels of autonomous expenditure and induced expenditure at income levels of 150 and 200. (d) In this same diagram show what would happen if autonomous expenditure increased by 20. Exercise 6.2 Suppose the media predicts a deep and persistent economic recession. Households expect their future income and employment prospects to fall. They cut back on expenditure, re- ducing autonomous expenditure from 50 to 30. (a) Re-draw the aggregate expenditure functions you have drawn in your diagrams for Exer- cise 6.1 to show the effects, if any, of this change in household behaviour. (b) Suppose the negative economic forecast also reduces induced expenditure in the economy from 0.75Y to 0.5Y. In a diagram show the effect would this have on the aggregate expendi- ture functions you have drawn. Exercise 6.3 Construct a table showing autonomous, induced and aggregate expenditure at differ- ent income levels (Y) for an economy with autonomous expenditure of 105 and induced expendi- ture of 0.5Y. (a) Using numbers from your table draw a diagram showing the aggregate expenditure function AE. What is the intercept of this function on the vertical axis? (b) What is the slope of the AE function, and what does the slope measure? (c) Write the equation for the aggregate expenditure function for this economy. Exercise 6.4 Output and income are in equilibrium when planned expenditures AE are equal to national income, Y', in other words, meaning Y = AE. (a) Suppose the AE function is AE = 175 +0.75Y. Draw a diagram showing the aggregate expenditure function. (b) In your diagram draw the 45 line that shows all points at which national income and aggre- gate expenditures are equal () = AE). 148 - Aggregate expenditure & aggregate demand (c) Using your diagram, or a numerical example, or an algebraic solution, find equilibrium output and income in this example and show it in the diagram.Exercise 6.5 The diagram below shows the aggregate expenditure schedule for the economy and the equilibrium condition on the 450 line. AE Y =AE F AE =C+I+X -IM E A Real GDP H & Income (a) Suppose output is OG. What is the level of planned aggregate expenditure? Is planned ex- penditure greater or less than output? (b) What is the size of the unplanned change in inventories at output OG? (c) How will business firms respond to this situation? (d) What is the equilibrium income and expenditure? (e) Suppose output is at OJ: What is there an unplanned change in inventories? Exercise 6.6 The following diagram shows an economy that initially has an aggregate expenditure function AK. Exercises for Chapter 6 . 149 AE Y -AE K Real GDP F G H & Income (a) What is the initial equilibrium real GDP? (b) Suppose there is an increase in the marginal propensity to import. What is the new aggregate expenditure function? (c) What is the new equilibrium real GDP and income? (d) Suppose, instead, the marginal propensity to consume has increased. What is the new aggre- gate expenditure function? What is the new equilibrium real GDP and income?Exercise 6.? The distinction between autonomous and induced expenditure is important for the determination of equilibrium real GDP. Assume that the marginal propensity spend on domes6c output is .".-'[l and autonomous aggregate expenditure is zero. {a} What is the equation for the aggregate expendinire function under these assumptions? {h} Draw the aggregate expenditure function in an incomeexpenditure 45\" line diagram. {c} What is the equilibrium level of real GDP illustrated by your diagram? {d} Explain why this is the equilibrium level of real GDP. Exercise 6.3 Suppose the slope of the AF. inction is I16. Starting from equilibrium, suppose planned investment increases by ill. {a} By how much and in what direction does equilibrium income change? {b} How much of that change in equilibrium income is the result of the change in induced ex- penditure'? {c} How would your answers to {h} differ if the slope of the AE inction was I13? 156! I Aggregate expenditure Sr. aggregate demand Exercise 6.9 Suppose autonomous expendinire is [ll and there is no induced expenditure in the economy. {a} Write the aggregate expenditure function for this economy. {h} Draw the aggregate expenditure function and the 45" line in a diagram. {c} What is the equilibrium level of real output and income? {d} By how much would equilibrium real output change if autonomous expenditure increased to 125'? Show the change in expenditure and equilibrium in your diagram for part {b}. {e} What is the size of the multiplier? Explain your