Eastwood's ECO285 assignments

1 a The marginal propensity to consume is 0.5.

The marginal propensity to consume is the fraction of a change in disposable income that is consumed. On Heron Island, when disposable income increases by $10 million per year, consumption expenditure increases by $5 million per year. The marginal propensity to consume is 0.5. 

1 b The table that shows Heron Island’s saving lists disposable income from zero to 40 in increments of 10. Against each level of disposable income are the amounts of saving, which equal disposable income minus consumption expenditure. These amounts run from –5 at zero disposable income to 15 at a disposable income of 40. For each increase in disposable income of $1, saving increases by 50 cents. 

1 c  The marginal propensity to save is 0.5

The marginal propensity to consume plus the marginal propensity to save equals 1. Because consumption expenditure and saving exhaust disposable income, 0.5 of each dollar increase in disposable income is consumed and the remaining part (0.5) is saved.

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2 a The marginal propensity to save is 0.1. 

The marginal propensity to save is the fraction of a change in disposable income that is saved. On Spendthrift Island, when disposable income increases by $500 million per year, saving increases by $50 million per year. The marginal propensity to save is 0.1.

2 b 

The table above shows Spendthrift Island’s consumption expenditure. It lists disposable income from zero to $3,000 million. Against each level of disposable income are the amounts of consumption expenditure, which equal disposable income minus saving. For each increase in disposable income of $1, consumption expenditure increases by 90 cents.

2 c  The marginal propensity to consume is 0.9.

The marginal propensity to consume plus the marginal propensity to save equals 1. Because consumption expenditure and saving exhaust disposable income, 0.9 of each dollar increase in disposable income is consumed and the remaining part (0.1) is saved.

2 d  Spendthrift Island is aptly named because the marginal propensity to consume is quite large. As the answer to the last part pointed out, from each additional dollar of income, 90 cents is spent on consumption expenditure and only 10 cents is saved.

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3 a Autonomous expenditure is $2 billion

Autonomous expenditure is expenditure that does not depend on real GDP. Autonomous expenditure equals the value of aggregate planned expenditure when real GDP is zero.

3 b  The marginal propensity to consume is 0.6. 

When the country has no imports (m=0) or exports and no income taxes (t=0), the slope of the AE curve {g=b(1-t)-m} equals the marginal propensity to consume. When income increases from 0 to $6 billion, aggregate planned expenditure increases from $2 billion to $5.6 billion. That is, when real GDP increases by $6 billion, aggregate planned expenditure increases by $3.6 billion. The marginal propensity to consume is $3.6 billion/$6 billion, which is 0.6.

3 c  From the graph, aggregate planned expenditure is $5.6 billion when real GDP is $6 billion.  Note that equilibrium expenditure is actually $5 billion, although it looks like about $4 billion on the graph in the text.

Equilibrium expenditure is the level of aggregate expenditure at which aggregate planned expenditure equals real GDP. In terms of the graph, equilibrium expenditure occurs at the intersection of the AE curve and the 45° line. Draw in the 45° line, and you'll see that the intersection occurs at about $4 billion. This is because the AE line is incorrectly drawn. It is not quite steep enough. If you solve for equilibrium, you will find Y = A/(1-g) = 2/(1-0.6) = 5, or $5 billion per year.

3 d  Inventories are being depleted.

When the real GDP is less than AE, production is lagging behind sales. The gap is filled by inventories, which are sold faster than they are replaced. Of course, the author of this question mistakenly thought that equilibrium was at Y = AE = $4 billion. Thus the answer in the back of the text reads that "there are no changes in inventories. When the economy is at equilibrium expenditure, inventories equal the planned level and there is no unplanned change in inventories."

3 e  Firms are accumulating inventories. That is, unplanned inventory investment is positive.

When real GDP is $6 billion, aggregate planned expenditure is less than real GDP, so firms cannot sell all that they produce. Inventories pile up.

3 f  The multiplier is 2.5.

The multiplier equals 1/(1 - g), where g is the slope of AE {g = b(1-t)-m = 0.6 (1-0) - 0 = 0.6}. The multiplier equals 1/(1 - 0.6), which equals 2.5.

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4 a  Autonomous expenditure equals 220 billion cloves per year. 

Autonomous expenditure equals the value of aggregate planned expenditure when real GDP is zero. Because the spreadsheet does not list GDP of zero, calculate the value of consumption expenditure and imports when GDP equals zero. From the spreadsheet, consumption expenditure falls by 60 billion cloves for every 100 billion clove decrease in GDP. Hence when GDP equals zero, autonomous consumption expenditure is 50 billion cloves. Similarly, from the spreadsheet, imports decrease by 15 billion cloves for every 100 billion clove decrease in GDP. Therefore when GDP equals zero, imports equal zero. Thus autonomous expenditure is 50 billion cloves (consumption expenditure) plus 50 billion cloves (investment) plus 60 billion cloves (government purchases) plus 60 billion cloves (exports) or 220 billion cloves.

4 b  The marginal propensity to consume is 0.6.

When income increases from 100 billion cloves to 200 billion cloves, consumption expenditure increases from 110 billion cloves to 170 billion cloves. Thus a 100 billion clove increase in GDP increases consumption expenditure by 60 billion cloves. Therefore the marginal propensity to consume is 60 billion cloves/100 billion cloves, which is 0.6.

4 c  Aggregate planned expenditure is 310 billion cloves.     Back to 1 2 3 4 5 6 7 8

Aggregate planned expenditure is the sum of consumption expenditure (170 billion cloves) plus planned investment (50 billion cloves) plus government purchases (60 billion cloves) plus exports (60 billion cloves) minus imports (20 billion cloves) or 310 billion cloves.

4 d  Inventories are decreasing so that unplanned inventory investment is negative.

When real GDP is 200 billion cloves, aggregate planned expenditure is 310 billion cloves. Because aggregate planned expenditure exceeds real GDP, firms sell all that they produce and more so that inventories are depleted.

4 e  Firms are accumulating inventories so that unplanned inventory investment is positive.

When real GDP is 500 billion cloves, aggregate planned expenditure is 445 billion cloves. Firms cannot sell all that they produce so that unplanned inventories pile up.

4 f  The multiplier equals 1.8181...

The multiplier equals 1/(1 - g), where g is the slope of AE {g = b(1-t)-m = 0.6 (1-0) - .15 = 0.45}. The multiplier equals 1/(1 - 0.45), which equals 1.8181.

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5 a  The consumption function is C = 100 + 0.9(Y – T). This simplifies to: C = -260 + 0.9Y

The consumption function is the relationship between consumption expenditure and disposable income, other things remaining the same. Disposable income , YD=Y-T. Substitute the lump-sum tax of T=$400 billion:

C = 100 + 0.9(Y – T).  Consumption as a function of disposable income.

C = 100 + 0.9(Y – 400). Substitute the lump-sum tax of T=$400

C = 100 + 0.9Y – 360

C = -260 + 0.9Y     Consumption as a function of real GDP. 

5 b  The equation of the AE curve is AE = 600 + 0.9Y, where Y is real GDP. 

Aggregate planned expenditure is the sum of consumption expenditure, investment, government purchases, and net exports (but X=M=0 here). Using the symbol AE for aggregate planned expenditure, aggregate planned expenditure is:

AE = a + b(Y – T) + I + G

AE = 100 + 0.9(Y – 400) + 460 + 400

AE = 100 + 0.9Y – 360 + 460 + 400 

AE = 600 + 0.9Y

5 c  Equilibrium expenditure is $6,000 billion.

Equilibrium expenditure is the level of aggregate expenditure that occurs when aggregate planned expenditure equals real GDP. That is,

AE = 600 + 0.9Y and AE = Y

Solving these two equations for Y gives equilibrium expenditure of $6,000 billion.

Y = 600 + 0.9Y

Y = 600 /(1-0.9) = 6000

5 d  Equilibrium real expenditure decreases by $1,000 billion, and the multiplier is 10.     

The multiplier equals 1/(1 - the slope of the AE curve). The equation of the AE curve tells us that the slope of the AE curve is 0.9. So the multiplier is 1/(1 - 0.9), which is 10. Then, the change in equilibrium expenditure equals the change in investment (360 - 460 = -100) multiplied by 10.

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6 a  The consumption function is C = 1 + 0.95(Y – T) where the “1” is 1 billion. 

The consumption function is the relationship between consumption expenditure and disposable income, other things remaining the same. The constant in the consumption function is autonomous consumption, $1 billion. The slope of the consumption function is the MPC, 0.95 in the case at hand. 

C = a + b(Y – T) Substitute for a and b 

C = 1 + 0.95(Y – T).  Consumption as a function of disposable income.

C = 1 + 0.95Y – .95T_a.  Distribute b; next substitute in the value of Ta

C = 1 + 0.95Y – 3.8

C = -2.8 + 0.95Y. Consumption as a function of real GDP.

6 b  The equation of the AE curve is AE = 5.2 + 0.95Y, where Y is real GDP.

Aggregate planned expenditure is the sum of consumption expenditure, investment, government purchases, and net exports. Net exports are zero. Then, using the symbol AE for aggregate planned expenditure, aggregate planned expenditure is:

AE = a +    b (Y – T) + I + G + X - M

AE = 1 + 0.95(Y – 4) + 4 + 4 + 0 + 0

AE = 1 + 0.95Y – 3.8 + 4 + 4

AE = 5.2 + 0.95Y

6 c  Equilibrium expenditure is $104 billion.

Equilibrium expenditure is the level of aggregate expenditure that occurs when aggregate planned expenditure equals real GDP. That is,

AE = 5.2 + 0.95Y and AE = Y. Solving these two equations for Y gives equilibrium expenditure of $104 billion.

Y = 5.2 + 0.95Y 

Y = 5.2 /(1-0.95) = 5.2 /0.05 = 104

6 d  Equilibrium real expenditure decreases by $20 billion (to $84 billion), and the multiplier is 20.

The multiplier equals 1/(1 - the slope of the AE curve). The equation of the AE curve tells us that the slope of the AE curve is 0.95. So the multiplier is 1/(1 - 0.95), which is 20. Then, the change in equilibrium expenditure equals the change in investment, -1 billion (3 - 4), multiplied by 20. The new equilibrium is 104 - 20 = $84 billion.

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7 a  The quantity demanded increases by $1,000 billion.

The increase in investment shifts the aggregate demand curve rightward by the change in investment times the multiplier. The multiplier is 10 and the change in investment is $100 billion, so the aggregate demand curve shifts rightward by $1,000 billion.

7 b  In the short-run, real GDP increases by less than $1,000 billion

Real GDP is determined by the intersection of the AD curve and the SAS curve. In the short run, the price level will rise and real GDP will increase but by an amount less than the shift of the AD curve.

7 c  In the long-run, real GDP will equal potential GDP, so real GDP does not increase.

Real GDP is determined by the intersection of the AD curve and the SAS curve. After the initial increase in investment, money wages increase, the SAS curve shifts leftward, and in the long run, real GDP moves back to potential GDP.

7 d  In the short run, the price level rises. In the long run, the price level rises.

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8 a  The quantity demanded increases by $20 billion.

The increase in investment shifts the aggregate demand curve rightward by the change in investment times the multiplier. The multiplier is 20 and the change in investment is $1 billion. Thus the aggregate demand curve shifts rightward by $20 billion.

8 b  In the long-run, real GDP equals potential GDP, so in the long run real GDP does not increase.

In the long run, the SAS curve shifts left (as wages rise to match in increase in prices) so that real GDP is determined by the intersection of the AD curve and the LAS curve. After the initial increase in investment, money wages increase and, as a result, the SAS curve shifts leftward. Eventually in the long run, real GDP moves back to equal potential GDP.

8 c  In the short run, the price level rises.

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