What is the equilibrium level of income given C = 100 + 0.75Y and I =

Understand the Problem

The question is asking to find the equilibrium level of income, given the consumption function C and an investment function I. The approach will involve setting the total output (income) equal to the total expenditure (C + I) and solving for Y.

Answer

The equilibrium level of income is $Y = \frac{100 + I}{0.25}$, where $I$ is the investment constant.

Steps to Solve

Identify the equations The consumption function is given as ( C = 100 + 0.75Y ), where ( C ) is consumption and ( Y ) is income. The investment function ( I ) is not defined, so we assume ( I ) is a constant, say ( I = I_0 ).
Setting up the equilibrium condition At equilibrium, total output (income) ( Y ) equals total expenditure, which is the sum of consumption and investment: $$ Y = C + I $$
Substituting the consumption function into the equilibrium condition Substitute ( C ) into the equilibrium equation: $$ Y = (100 + 0.75Y) + I_0 $$
Rearranging the equation Rearranging the equation to isolate ( Y ): $$ Y - 0.75Y = 100 + I_0 $$
Combining like terms Combine the ( Y ) terms: $$ 0.25Y = 100 + I_0 $$
Solving for income ( Y ) To find ( Y ), divide both sides by 0.25: $$ Y = \frac{100 + I_0}{0.25} $$
Calculating the equilibrium income Assuming ( I_0 ) is defined or needs to be assumed (e.g., if ( I_0 = 50 )): $$ Y = \frac{100 + 50}{0.25} = \frac{150}{0.25} = 600 $$

The equilibrium level of income, assuming ( I = 50 ), is ( Y = 600 ).

More Information

This equilibrium condition tells us how much total income is generated at the point where all income equals spending. The consumption function represents the behavior of consumers in the economy, while the investment function influences total demand.

Tips

Assuming ( I ) is zero if not specified, rather than using a defined constant.
Failing to correctly rearrange the equation to isolate ( Y ).

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