In an economy, the consumption function is C = 100 + 0.7Y, and investment is fixed at I = 200.

For simplicity, assume that this is a closed economy with no government.

Find the value of equilibrium income (or output) in this economy.

Question

In an economy, the consumption function is C = 100 + 0.7Y, and investment is fixed at I = 200.

For simplicity, assume that this is a closed economy with no government.

Find the value of equilibrium income (or output) in this economy.

BlackTom AI · Accepted Answer

We start by restating the given model and identifying what equilibrium means in this closed economy with no government: aggregate demand (AD) must equal output (Y). AD is C + I, since there is no government spending or net exports in this simplified setup.

First, write the consumption function and investment: C = 100 + 0.7Y, I = 200.

Set up the equilibrium condition: Y = C + I.
Substitute the expressions for C and I into the equilibrium equation: Y = (100 + 0.7Y) + 200.
Combine constants on the right-hand side and group Y terms: Y = 300 + 0.7Y.
To isolate Y, subtract 0.7Y from both sides: Y − 0.7Y = 300.
This gives 0.3Y = 300. Solving for Y involves dividing both sides by 0.3: Y = 300 / 0.3 = 1000.

Thus, the equilibrium level of income/output in this economy is 1000. Note that this result comes directly from balancing planned spending with production in a simple multiplier framework where the marginal propensity to consume is 0.7 and autonomous spending comprises the 100 units of autonomous consumption plus 200 units of investment.

ECON 2020-001 Spring 2025 Exam (Midterm 1)

In an economy, the consumption function is C = 100 + 0.7Y, and investment is fixed at I = 200. For simplicity, assume that this is a closed economy with no government. Find the value of equilibrium income (or output) in this economy.

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