Q.Suppose that for a particular economy, investment is equal to 200, government purchases are 150, net taxes (that is lump-sum taxes minus transfers) is 100 and consumption is given by $C = 100 + 0.75\,Y$.

In a three-sector economy, the equilibrium level of income is determined where aggregate demand ($AD = C + I + G$) equals aggregate supply ($Y$).

1. To find the equilibrium income, first express the consumption function in terms of total income $Y$. Given $C = 100 + 0.75\,Y_d$ and net taxes $T = 100$, disposable income is $Y_d = Y - T = Y - 100$. Substituting $Y_d$: $C = 100 + 0.75(Y - 100) = 100 + 0.75Y - 75 = 25 + 0.75Y$ Now, set $Y = C + I + G$: $Y = (25 + 0.75Y) + 200 + 150$ $Y = 375 + 0.75Y$ $Y - 0.75Y = 375$ $0.25Y = 375$ $Y = \frac{375}{0.25} = 1500$
2. The Marginal Propensity to Consume (MPC) from the consumption function $C = 100 + 0.75\,Y_d$ is $0.75$.

   The government expenditure multiplier ($k_G$) is $k_G = \frac{1}{1 - MPC}$.

   The tax multiplier ($k_T$) is $k_T = \frac{-MPC}{1 - MPC}$.

   $k_G = \frac{1}{1 - 0.75} = \frac{1}{0.25} = 4$

   $k_T = \frac{-0.75}{1 - 0.75} = \frac{-0.75}{0.25} = -3$ …

In macroeconomics, the equilibrium level of income in an economy is reached when the total amount of goods and services produced (aggregate supply) equals the total amount of goods and services demanded (aggregate demand). This is a fundamental concept in Keynesian economics, where aggregate demand drives the level of output and employment in the short run. For an economy with households, firms, and a government (a three-sector model), aggregate demand is the sum of consumption ($C$), investment ($I$), and government purchases ($G$).

The consumption function, $C = 100 + 0.75\,Y$, tells us that autonomous consumption (consumption independent of income) is 100, and the marginal propensity to consume (MPC) is 0.75. This means that for every additional rupee of disposable income, households spend 75 paise and save 25 paise. Net taxes ($T$) reduce disposable income, which in turn affects consumption.

(a) What is the level of equilibrium income?

The equilibrium condition for a three-sector economy states that aggregate supply ($Y$) must equal aggregate demand ($C + I + G$). Disposable income ($Y_d$) is total income ($Y$) minus net taxes ($T$).

1. Substitute the given values into the consumption function: We are given $C = 100 + 0.75\,Y$. However, this is a simplified form. Since net taxes ($T$) are present, consumption depends on disposable income ($Y_d = Y - T$). So, the consumption function should be $C = 100 + 0.75(Y - T)$. Given $T = 100$, $I = 200$, and $G = 150$.

2. Substitute the modified consumption function and other components into the equilibrium condition:

3. Solve for $Y$:

(b) Calculate the value of the government expenditure multiplier and the tax multiplier.

Multipliers describe how a change in an autonomous component of aggregate demand (like government expenditure or taxes) leads to a larger change in equilibrium income. This "multiplier effect" arises because an initial change in spending creates income for someone, who then spends a portion of that income, creating further income, and so on.

1. Identify the MPC:

   From the consumption function $C = 100 + 0.75\,Y$, the marginal propensity to consume (MPC) is $0.75$.

2. Calculate the government expenditure multiplier ($k_G$):

$$k_G = 4$$ …