Keynesian Analysis of an Economy

The Keynesian model provides insights into how an economy operates in the short run, emphasizing the role of aggregate demand in determining equilibrium output and income. In this scenario, let’s delve into the given information and address the questions using the Keynesian framework.

Consumption Function Graph

The consumption function is given by C = 200 + 0.8(Y – T), where Y represents disposable income and T denotes taxes. The graph of the consumption function is upward-sloping, with a slope of 0.8. The vertical intercept is 200, signifying autonomous consumption, and the slope of 0.8 indicates the marginal propensity to consume out of disposable income. As disposable income increases, consumption expenditure also rises, but not as steeply. Taxes, being autonomous at $10, lead to a parallel shift upwards of the consumption function by $10.

 Equilibrium National Income (Ye)

Equilibrium occurs when aggregate demand (Y) equals aggregate supply (production). In this scenario, aggregate demand consists of consumption (C), investment (I), government spending (G), and net exports (X – M). Given that investment spending (I) is $50, government spending (G) is $100, and net exports (X – M) are $20 at every level of disposable income, the aggregate demand function can be expressed as:

Y = C + I + G + (X – M) Y = (200 + 0.8(Y – T)) + 50 + 100 + 20

Solving for equilibrium income (Ye) yields: Y = 200 + 0.8(Y – 10) + 50 + 100 + 20 Y = 370 + 0.8Y – 8 0.2Y = 362 Y = 1810

Hence, the equilibrium national income (Ye) is $1810.

Government Budget Balance

The government budget balance is the difference between government revenues and government expenditures. Given that government spending (G) is constant at $100 and taxes (T) are $10, the budget balance is: Budget Balance = T – G Budget Balance = 10 – 100 Budget Balance = -90

The negative budget balance of $90 indicates that the government is running a deficit, where expenditures exceed revenues. This suggests that the government is borrowing to cover the deficit.

 Full Employment and Inventories

Full employment output (Yf) is given as $2000. If the economy is producing at the full employment level of output, any level of output beyond $2000 would lead to excess production, causing inventories to accumulate. Conversely, if output is below $2000, inventories would be depleted.

Keynesian 45° Diagram

On a Keynesian 45° diagram, we can depict equilibrium national income (Ye) and full employment output (Yf). Ye is at $1810 and Yf is at $2000. The gap between these two points represents the output gap. In this case, it’s negative, indicating that the economy is producing below its full employment potential.

Attaining Full Employment Income

To achieve full employment income (Ye = $2000), the government can use fiscal policy by increasing government spending (G). The change in equilibrium income (∆Y) can be calculated using the multiplier. The multiplier, in this case, is the reciprocal of the marginal propensity to consume (MPC), which is 0.8.

∆Y = (1 / (1 – MPC)) * ∆G ∆Y = (1 / (1 – 0.8)) * (2000 – 1810) ∆Y = (1 / 0.2) * 190 ∆Y = 950

Thus, the government would need to increase spending (∆G) by $950 to attain full employment income.

In conclusion, the Keynesian model provides a framework for analyzing how different economic components interact to determine equilibrium output and income. By examining the consumption function, government budget, and full employment output, we can assess the economy’s status, identify gaps, and formulate policies to achieve desired outcomes. In this scenario, a deficit budget reflects government borrowing, while the output gap indicates potential room for growth. To achieve full employment income, an increase in government spending is required, leveraging the multiplier effect to stimulate economic activity.