# Exercises for Chapter 6

Exercise 6.1 Suppose that in an economy with no government the consumption function is: $$C = 50 + 0.75Y$$.

(a) Draw a diagram showing the consumption function, and indicate the level of consumption expenditure when income is 150.

(b) In this same diagram, show what would happen to consumption expenditure if income increased to 200.

(c) Write the equation for the saving function and draw the saving function in a diagram.

(d) In this diagram show what would happen to savings if income increased from 200 to 250.

Exercise 6.2

(a) 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, reducing autonomous expenditure from 50 to 30. Re-draw the consumption and saving functions you have drawn in your diagrams for Exercise 6.1 to show the effects, if any, of this change in household behaviour.

(b) Suppose households also reduce the amount by which they are willing to spend out of any increase in income. In a diagram show the effect would this have on the consumption and savings functions you have drawn?

Exercise 6.3 The consumption function is $$C = 50 + 0.75Y$$ and investment is $$I = 50$$, exports are $$X = 25$$ and the import function is $$IM = 20 + 0.25Y$$.

(a) Write the equation for the aggregate expenditure function for this economy?

(b) Draw a diagram showing the aggregate expenditure function AE. What is the intercept of this function on the vertical axis?

(c) What is the slope of the AE function, and what does the slope measure?

Exercise 6.4 Output and income are in equilibrium when planned expenditures $$C + I + X − IM$$ are equal to national income, in other words, meaning $$Y = \text{AE}$$.

(a) Suppose the consumption function is $$C = 100 + 0.8Y$$, investment is 25, exports are 30 and imports are $$IM = 10 + 0.05Y$$. 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 aggregate expenditures are equal $$(Y = \text{AE})$$.

(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 45° line.

(a) Suppose output is 0G. What is the level of planned aggregate expenditure? Is planned expenditure greater or less than output?

(b) What is the size of the unplanned change in inventories at output 0G?

(c) How will business firms respond to this situation?

(d) What is the equilibrium income and expenditure?

(e) Suppose output is at 0J: 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.

(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 aggregate expenditure function? What is the new equilibrium real GDP and income?

Exercise 6.7 The distinction between autonomous and induced expenditure is important for the determination of equilibrium real GDP. Assume that the marginal propensity to consume is 0.80, the marginal propensity to import is 0.10 and autonomous aggregate expenditure is zero.

(a) What is the equation for the aggregate expenditure function under these assumptions?

(b) Draw the aggregate expenditure function in an income-expenditure 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 6.8 Suppose the marginal propensities to consume and import are 0.75 and 0.25. Starting from equilibrium, suppose planned investment increases by 10.

(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 consumption expenditure?

(c) How would your answers to (b) differ if the marginal propensity to consume were 0.85 rather than 0.75?

Exercise 6.9 Research by a team of expert economists has uncovered the consumption and import functions and produced a forecast of planned investment and exports for the economy of Wonderland as reported below.

(a) What equilibrium real GDP would Wonderland produce?

(b) What are the marginal propensities to consume and import in Wonderland?

(c) What is the size of the multiplier?

(d) If actual GDP were 900, what difference between planned and actual investment would result? Why?

(e) If planned investment increased by 50 to 100, what would happen to equilibrium income?

Exercise 6.10 Planned investment is 100, exports are 50 and saving is $$S = −25 + 0.2Y$$ and imports are $$IM = 25 + 0.3Y$$.

(a) Draw a diagram showing the initial equilibrium level of income.

(b) Now households decide to increase their saving at every level of income, but do not change their marginal propensity to save. Using the diagram show what happens to equilibrium income and to household saving?

Exercise 6.11 Suppose there is no autonomous expenditure in the economy. The aggregate expenditure function is $$\text{AE} = 0.75Y$$.

(a) Draw the aggregate expenditure function and the 45° line in a diagram.

(b) What is the equilibrium level of real output and income?