In an economy, the consumption function is C = 200 + 0.7Y, and investment is fixed at I = 400.

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 = 200 + 0.7Y, and investment is fixed at I = 400.

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

Let’s begin by identifying what equilibrium income means in this simple closed economy with no government: total output Y must equal total demand, which is consumption C plus investment I.
First, write down the given consumption function: C = 200 + 0.7Y. Investment is fixed at I = 400. Since there is no government or foreign sector, aggregate demand AD = C + I.
Set up the equilibrium condition: Y = AD = C + I = (200 + 0.7Y) + 400.
Simplify the equation by combining constants: Y = 600 + 0.7Y.
To isolate Y, subtract 0.7Y from both sides: Y − 0.7Y = 600, which gives 0.3Y = 600.
Solve for Y by dividing both sides by 0.3: Y = 600 / 0.3 = 2000.
Now, verify the result by plugging back into the components: C = 200 + 0.7×2000 = 200 + 1400 = 1600, and with I = 400, AD = 1600 + 400 = 2000, which matches Y, confirming equilibrium.
Alternative check (conceptual): the multiplier in this simple model is 1 / (1 − marginal propensity to consume) = 1 / (1 − 0.7) = 1 / 0.3 ≈ 3.333. The autonomous spending component (the intercepts) totals 600, so Y = 3.333 × 600 ≈ 2000, consistent with the calculation above.
If you were to modify any component, such as increasing I or changing the MPC, you would shift the equilibrium Y accordingly, but with the given numbers the balance works out cleanly at Y = 2000.

In an economy, the consumption function is C = 200 + 0.7Y, and investment is fixed at I = 400. For simplicity, assume that this is a closed economy with no government. Find the value of equilibrium income (or output) in this economy.数值题

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