An economy is described by the following equations:

C = 1600 + 0.8(Y – T)

I = 1000

G = 1800

T = 3000 + 0.01 Y

What is the equilibrium level of output in this economy?

Question

An economy is described by the following equations:

C = 1600 + 0.8(Y – T)

I = 1000

G = 1800

T = 3000 + 0.01 Y

What is the equilibrium level of output in this economy?

BlackTom AI · Accepted Answer

To evaluate the equilibrium output, I start from the national income identity: Y = C + I + G, using the given components of consumption, investment, government spending, and taxes.
Option A: 7600.5. If we plug into Y = C + I + G, we need C = 1600 + 0.8(Y − T) with T = 3000 + 0.01Y. This yields C = 1600 + 0.8(0.99Y − 3000) = 0.792Y − 800, so Y = (0.792Y − 800) + 1000 + 1800 = 0.792Y + 2000. Solving 0.208Y = 2000 gives Y ≈ 9615.38, not 7600.5, so this option is inconsistent with the model.
Option B: 7650.4. Using the same derivation, the equilibrium condition 0.208Y = 2000 leads to Y ≈ 9615.38, which differs from 7650.4. Therefore this value does not satisfy the equations.
Option C: 8420.5. Again, applying Y = 0.792Y + 2000 and solving for Y yields 0.208Y = 2000, so Y ≈ 9615.38. 8420.5 does not solve the equilibrium condition, so this is not correct.
Option D: 9615.4. This value closely matches the solution to 0.208Y = 2000, since Y = 2000 / 0.208 ≈ 9615.38. The arithmetic aligns with the derived identity Y = 0.792Y + 2000, which rearranges to 0.208Y = 2000, giving Y ≈ 9615.38, consistent with 9615.4 when rounded.
In summary, the key step is substituting T into C, simplifying to C = 0.792Y − 800, then summing C + I + G to get Y = 0.792Y + 2000, which leads to 0.208Y = 2000 and Y ≈ 9615.38. The option closest to this result is 9615.4, while the other choices fail to satisfy the equilibrium condition derived from the model.

ECON10003_2025_SM1 Pre-Tutorial Quiz 4

An economy is described by the following equations: C = 1600 + 0.8(Y – T) I = 1000 G = 1800 T = 3000 + 0.01 Y What is the equilibrium level of output in this economy?

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