Key Concept: Formula Application

c) 4

[Solution Description]

The formula for calculating the multiplier is given by:

$$\text{Multiplier} = \frac{1}{1 – \text{mpc}}$$

Substituting the value of $$\text{mpc} = 0.75$$ into the formula, we get:

$$\text{Multiplier} = \frac{1}{1 – 0.75} = \frac{1}{0.25} = 4$$

Therefore, the correct answer is 4.

Key Concept: Real-world Application

b) Increase in aggregate demand

[Solution Description]

Increasing autonomous consumption by providing direct subsidies leads to an immediate increase in consumer spending, causing an increase in aggregate demand. This stimulates economic activity as more goods and services are purchased.

Key Concept: Marginal Propensity to Consume

c) 0.75

[Solution Description] The marginal propensity to consume (MPC) is calculated as the change in consumption divided by the change in income:

$$\text{MPC} = \frac{\Delta C}{\Delta Y}$$

Where $$\Delta C = 550 – 400 = 150$$ and $$\Delta Y = 700 – 500 = 200$$.

$$\text{MPC} = \frac{150}{200} = 0.75$$

Therefore, the MPC is 0.75.

Key Concept: Fixed Price Level

b) Due to unused resources

[Solution Description] The assumption of fixed price levels allows for simplifying calculations by avoiding complications introduced by changing prices. It often reflects situations where resources are underemployed, so price changes do not occur immediately.

Key Concept: Comparative Analysis

c) \$120

[Solution Description] The change in income $$\Delta Y$$ is:

$$\Delta Y = 1200 – 1000 = 200$$

The change in induced consumption $$\Delta C$$ can be calculated using the formula $$\Delta C = c \times \Delta Y$$. Substituting the values:

$$\Delta C = 0.6 \times 200 = 120$$

Hence, the change in induced consumption is \$120.

Key Concept: Advanced Calculation, Scenario Analysis

c) \$80

[Solution Description]

The initial consumption function is given by $$C = 50 + 0.6Y$$.

When autonomous consumption increases by \$20, the new consumption function becomes $$C’ = 70 + 0.6Y$$.

With an increase in income of \$100, the change in induced consumption can be calculated using the marginal propensity to consume (MPC), which is 0.6:

Change in induced consumption $$= 0.6 \times 100 = \$60$$.

Hence, the total change in consumption due to both factors is:

$$\Delta C = (Increase \ in \ Autonomous \ Consumption) + (Change \ in \ Induced \ Consumption)$$

$$\Delta C = 20 + 60 = \$80$$.

Therefore, the total consumption changes by \$80.

Key Concept: Derivation of Relationships, Complex Problem Solving

c) \$500 million

[Solution Description] The consumption function is given by $$C = C + cY$$, where $$C$$ is the total consumption, $$C$$ is autonomous consumption, $$c$$ is MPC, and $$Y$$ is income.

First, calculate induced consumption using the formula:

$$cY = 0.6 \times 500 \text{ million} = 300 \text{ million}$$

Now, add autonomous consumption to find total consumption:

$$C = 200 \text{ million} + 300 \text{ million} = 500 \text{ million}$$

Therefore, the new level of total consumption is \$500 million.

Key Concept: Concept Identification

a) Demand is more than full employment level

[Solution Description]

Excess demand occurs when the aggregate demand in an economy surpasses the full employment level of output, leading to inflationary pressure. Thus, the scenario where demand exceeds the full employment level represents excess demand.

Key Concept: Definition Recall

b) Equilibrium

[Solution Description]

The intersection point on an aggregate demand and supply graph represents equilibrium, where the quantity of goods demanded equals the quantity of goods supplied.

Key Concept: Cause and Effect

b) Aggregate demand increases

[Solution Description] An increase in autonomous investment raises aggregate demand because it represents additional spending in the economy that is independent of income. This increase in spending leads to a higher equilibrium level of income and output, thereby boosting aggregate demand.

Key Concept: Basic Concept

c) The equilibrium level of income increases.

[Solution Description] When aggregate demand increases, firms respond by increasing production to meet the higher demand. This leads to an increase in both output and income, moving the economy to a new equilibrium with a higher level of income.

Key Concept: Marginal Propensity to Consume

b) \$90

[Solution Description] The marginal propensity to consume (MPC) defines how much consumption changes with a change in income. Given MPC = 0.6 and an increase in income of \$150, the change in consumption ($$\Delta C$$) can be calculated using the formula:

$$\Delta C = MPC \times \Delta Y$$

where $$\Delta Y$$ is the change in income. Substituting the values, we get:

$$\Delta C = 0.6 \times 150 = 90$$

Therefore, the change in consumption is \$90. The correct answer is option b.

Key Concept: Deficient Demand

d) Rise in unemployment rate

[Solution Description] Persistent deficient demand means that aggregate demand is less than what is needed to achieve full employment, leading to unemployment and downward pressure on prices. This is because there are insufficient opportunities for firms to sell their goods and services, resulting in reduced production and layoffs.

Key Concept: Concept Identification

c) The multiplier effect increases.

[Solution Description] When the marginal propensity to consume (mpc) increases, the denominator in the multiplier formula $$\left(\frac{1}{1 – \text{mpc}}\right)$$ decreases, resulting in a larger multiplier. This means that for a given change in investment, the total increase in output becomes larger as mpc increases.

Key Concept: Role of Multiplier

c) Increase by \$250

[Solution Description] The multiplier $$k$$ is defined as $$\frac{1}{1-c}$$, where $$c$$ is the marginal propensity to consume. Given that $$c = 0.8$$:

$$k = \frac{1}{1-0.8} = \frac{1}{0.2} = 5$$

The change in equilibrium income due to a change in autonomous expenditure is calculated as follows:

$$\Delta Y = k \times \Delta AE$$

Here, $$\Delta AE = 50$$:

$$\Delta Y = 5 \times 50 = 250$$

Thus, the equilibrium income increases by \$250.

Key Concept: 45-Degree Line

b) Equilibrium

[Solution Description]

The 45-degree line in macroeconomic graphs represents situations where aggregate supply equals aggregate demand. When plotted, it shows points at which the economy is in equilibrium because production matches planned expenditure.

Key Concept: Consumption Function Components

b) Marginal propensity to consume

[Solution Description] In the consumption function $$C = C + cY$$, ‘c’ represents the marginal propensity to consume (MPC). It indicates how much consumption changes with a change in income.

Key Concept: Complex Calculation, Series Summation

c) \$800 million

[Solution Description]

The formula for the multiplier effect is given by $$\frac{1}{1-c}$$, where $$c$$ is the MPC.

$$\text{Multiplier} = \frac{1}{1 – 0.75} = \frac{1}{0.25} = 4$$

The total increase in national income is then calculated as:

$$\text{Total Increase} = 4 \times 200 = 800 \text{ million dollars}$$

Thus, the total increase in national income is \$800 million.

Key Concept: Autonomous Change Impact, Government’s Fiscal Role

c) The aggregate demand curve could shift either way depending on the magnitude of changes.

[Solution Description] An increase in government expenditure shifts the aggregate demand curve to the right due to higher fiscal stimulus. A decrease in autonomous investment shifts it downward because it lowers the investment component of aggregate demand. The net effect depends on which factor dominates.

Key Concept: Function Identification

b) $$C = C + cY$$

[Solution Description] The consumption function in the graphical method is generally represented as $$C = C + cY$$, where $$C$$ is autonomous consumption, and $$cY$$ indicates induced consumption dependent on income level.

Key Concept: Complex Equilibrium Analysis, Multiplier Calculation

b) \$50 billion

[Solution Description] To find the change in equilibrium national income, we need to calculate the spending multiplier and the tax multiplier effect. The formula for the spending multiplier is:

$$\text{Spending Multiplier} = \frac{1}{1 – \text{MPC}} = \frac{1}{1 – 0.75} = 4$$

The change in income due to increased government expenditure (\$\Delta G\$) of \$20 billion is calculated as:

$$\Delta Y_G = \text{Spending Multiplier} \times \Delta G = 4 \times 20 = 80 \text{ billion}$$

The formula for the tax multiplier is $$-\frac{\text{MPC}}{1 – \text{MPC}}$$. Therefore,

$$\text{Tax Multiplier} = -\frac{0.75}{1 – 0.75} = -3$$

The change in income due to increased taxes (\$\Delta T\$) of \$10 billion is:

$$\Delta Y_T = \text{Tax Multiplier} \times \Delta T = -3 \times 10 = -30 \text{ billion}$$

The total change in equilibrium income is:

$$\Delta Y = \Delta Y_G + \Delta Y_T = 80 – 30 = 50 \text{ billion}$$

Thus, the resulting change in equilibrium national income is \$50 billion.

Key Concept: Equilibrium Condition

b) Aggregate demand equals aggregate supply

[Solution Description] For the final goods market to be in equilibrium, the total output (Y) must equal aggregate demand (C + I). This occurs when planned expenditure matches actual expenditure, meaning there are no unintended increases or decreases in inventories.

Key Concept: Inventory Investment Impact

c) If actual inventories exceed planned inventories, firms may reduce production.

[Solution Description] When planned inventory investment differs from actual inventory investment, firms will adjust their production levels to bring inventories back in line. If planned inventory exceeds actual, it indicates demand is greater than expected, leading to increased production.

Key Concept: Identify Components

b) Autonomous Consumption

[Solution Description] The consumption function is expressed as $$C = C + cY$$, where $$C$$ is autonomous consumption and $$cY$$ reflects the marginal propensity to consume multiplied by income.

Key Concept: Slope Identification

c) $$c$$ (marginal propensity to consume)

[Solution Description] The slope of the aggregate demand function is the same as the slope of the consumption function, which is represented by $$c$$ (the marginal propensity to consume).

Key Concept: Aggregate Demand

d) Consumption

[Solution Description] Aggregate demand comprises various components such as consumption, investment, government spending, and net exports. Among the options, only consumption is part of aggregate demand.

Key Concept: Aggregate Demand Decrease

c) 75

[Solution Description] The decrease in aggregate demand is calculated using the formula $$(MPC_{initial} – MPC_{new}) \times Y$$. Substitute the values:

$$(0.8 – 0.5) \times 250 = 0.3 \times 250 = 75.$$

Thus, the aggregate demand decreased by 75 units.

Key Concept: Cause and Effect

c) Equilibrium quantity increases

[Solution Description] An improvement in production technology typically lowers the cost of producing goods, increasing the supply of the product. Ceteris Paribus, this leads to an increase in the equilibrium quantity in the market, as producers can supply more at every price point.

Key Concept: Investment Function

b)

[Solution Description]

In economic models, the investment function $$I = I$$ indicates that investment is constant and does not change with the level of income. Therefore, its graphical representation is a horizontal line, showing no relationship between investment and income levels.

Key Concept: Advanced Application, Critical Analysis

c) Total aggregate demand increases by \$150 billion

[Solution Description] To determine the impact, we apply the balanced budget multiplier concept. When both government spending (G) and taxes (T) increase equally, the balanced budget multiplier indicates that the overall effect on aggregate demand equals the change in government spending because $$MPC \cdot \Delta(G-T) = 0.9 \cdot 0 = 0$$.

The change in aggregate demand due to government spending alone is given by:

$$\Delta AD = \Delta G = 150 \text{ billion dollars}$$

Thus, the increase in aggregate demand is exactly \$150 billion since the balanced budget multiplier is 1 when considering the full theoretical context and implications.

Key Concept: Graphical Shift Analysis

a) Shifts upwards

[Solution Description]

An increase in government spending leads to an increase in aggregate demand. This causes the aggregate demand curve to shift upwards or to the right. The increased spending raises the total expenditure in the economy, increasing the equilibrium output level.

Key Concept: Definition Recall

b) It remains constant regardless of income

[Solution Description]

Autonomous investment refers to the portion of total investment that remains unchanged regardless of the level of national income or output. It is constant.

Key Concept: Demand Fluctuations

c) Assertion is true, but Reason is false.

[Solution Description] The assertion states that a decrease in aggregate demand leads to an output level lower than the full employment level. This is true as deficient demand can cause unemployment and reduce output. However, the reason provided suggests that prices adjust downward to restore full employment. In the context of fixed price levels assumed in short-run analysis, this reasoning is false because prices are not flexible enough to automatically restore full employment.

Key Concept: Direct Application

c) 125 units

[Solution Description] To find the change in equilibrium income, use the formula for the multiplier $$k = \frac{1}{1 – MPC}$$, and then multiply this by the change in autonomous spending.

Calculating the multiplier:

$$k = \frac{1}{1 – 0.6} = \frac{1}{0.4} = 2.5$$

Change in equilibrium income = Multiplier $$\times$$ Change in autonomous spending:

$$\Delta Y = 2.5 \times 50 = 125$$

Therefore, the equilibrium income increases by 125 units.

Key Concept: Application of Formula

d) \$250

[Solution Description]

The formula for the total increase in output due to an initial change in autonomous expenditure $$\Delta A$$ is given by:

$$\text{Total Increase in Output} = \frac{\Delta A}{1 – c}$$

Here, $$\Delta A = 50$$ and $$c = 0.8$$. Substituting these into the formula:

$$\text{Total Increase in Output} = \frac{50}{1 – 0.8} = \frac{50}{0.2} = 250$$

Therefore, the total increase in output is \$250.

Key Concept: Comparative Analysis

c) Equilibrium output decreases more than the decrease in investment

[Solution Description] The relationship between changes in autonomous investment and equilibrium output is determined by the multiplier effect. The multiplier ($$k$$) is given by $$k = \frac{1}{MPS}$$. With $$MPS = 0.25$$, the multiplier is:

$$k = \frac{1}{0.25} = 4$$

A decrease in investment leads to a multiplied decrease in equilibrium output. For example, a \$10 billion decrease in investment would reduce equilibrium output by:

$$\Delta Y = 4 \times (-10) = -40$$

Thus, the equilibrium output decreases by \$40 billion due to a \$10 billion reduction in autonomous investment.

Key Concept: Cause and Effect

b) Rise in prices

[Solution Description]

In the long run, excess demand typically leads to a rise in prices. This is because when demand outstrips supply at the current price levels, it creates upward pressure on prices until a new equilibrium is reached where demand matches supply.