Question:
Suppose the estimated consumption equation of an economy is:
\[
C = 40 + \beta Y_d
\]
where \(Y_d\) is the personal disposable income, \(\beta\) is the marginal propensity to consume (MPC). Government expenditure \(G\) is given as 90. Total tax (\(T_x\)) received is \(\delta Y\), where \(Y\) is aggregate output or real income and \(\delta\) is tax to real income proportionality factor. Autonomous investment \(I_A\) is given as 80. What are the tax revenue and budget surplus of the government when \(\beta = 0.75\) and \(\delta = 0.20\)? All units are measured in constant rupees.
Suppose the estimated consumption equation of an economy is:
\[
C = 40 + \beta Y_d
\]
where \(Y_d\) is the personal disposable income, \(\beta\) is the marginal propensity to consume (MPC). Government expenditure \(G\) is given as 90. Total tax (\(T_x\)) received is \(\delta Y\), where \(Y\) is aggregate output or real income and \(\delta\) is tax to real income proportionality factor. Autonomous investment \(I_A\) is given as 80. What are the tax revenue and budget surplus of the government when \(\beta = 0.75\) and \(\delta = 0.20\)? All units are measured in constant rupees.
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The tax revenue and budget surplus are determined by the equilibrium income \(Y\), the marginal propensity to consume \(\beta\), and the tax rate \(\delta\).
Updated On: Nov 21, 2025
- Tax revenue = Rs. 105 and surplus = Rs. 15
- Tax revenue = Rs. 118 and surplus = Rs. 28
- Tax revenue = Rs. 110 and surplus = Rs. 20
- ax revenue = Rs. 125 and surplus = Rs. 35
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The Correct Option is A
Solution and Explanation
Step 1: Set up the economy's components.
From the consumption equation \(C = 40 + \beta Y_d\), we know that consumption depends on the personal disposable income \(Y_d\). We are given that \(G = 90\), \(I_A = 80\), \(\beta = 0.75\), and \(\delta = 0.20\). Government tax revenue \(T_x = \delta Y = 0.20Y\). Step 2: Calculate aggregate output \(Y\).
The equilibrium condition in the economy is: \[ Y = C + I_A + G \] Substituting the consumption function \(C = 40 + 0.75Y_d\) where \(Y_d = Y - T_x\), we get: \[ C = 40 + 0.75(Y - 0.20Y) \] Simplifying: \[ C = 40 + 0.75(0.80Y) = 40 + 0.60Y \] Now, substitute into the equilibrium equation: \[ Y = 40 + 0.60Y + 80 + 90 \] Simplifying further: \[ Y - 0.60Y = 210 \] \[ 0.40Y = 210 \] \[ Y = 525 \] Step 3: Calculate tax revenue and surplus.
Tax revenue \(T_x = 0.20Y = 0.20 \times 525 = 105\). The budget surplus is the difference between government expenditure and tax revenue: \[ \text{Surplus} = T_x - G = 105 - 90 = 15 \] Step 4: Conclusion.
The correct answer is (A), with tax revenue of Rs. 105 and a budget surplus of Rs. 15.
From the consumption equation \(C = 40 + \beta Y_d\), we know that consumption depends on the personal disposable income \(Y_d\). We are given that \(G = 90\), \(I_A = 80\), \(\beta = 0.75\), and \(\delta = 0.20\). Government tax revenue \(T_x = \delta Y = 0.20Y\). Step 2: Calculate aggregate output \(Y\).
The equilibrium condition in the economy is: \[ Y = C + I_A + G \] Substituting the consumption function \(C = 40 + 0.75Y_d\) where \(Y_d = Y - T_x\), we get: \[ C = 40 + 0.75(Y - 0.20Y) \] Simplifying: \[ C = 40 + 0.75(0.80Y) = 40 + 0.60Y \] Now, substitute into the equilibrium equation: \[ Y = 40 + 0.60Y + 80 + 90 \] Simplifying further: \[ Y - 0.60Y = 210 \] \[ 0.40Y = 210 \] \[ Y = 525 \] Step 3: Calculate tax revenue and surplus.
Tax revenue \(T_x = 0.20Y = 0.20 \times 525 = 105\). The budget surplus is the difference between government expenditure and tax revenue: \[ \text{Surplus} = T_x - G = 105 - 90 = 15 \] Step 4: Conclusion.
The correct answer is (A), with tax revenue of Rs. 105 and a budget surplus of Rs. 15.
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