Indicate the equilibrium level of output in an economy where: C = 180 + 0.5 Yd I = 100 G = 160 T = 120

Question

BlackTom AI · Accepted Answer

To begin, I’ll identify the key components of the economy: consumption, investment, and government spending, while accounting for taxes that affect disposable income.
Option by option, consider how the equilibrium output is determined in a simple closed economy with taxes: Y = C + I + G, where C depends on disposable income Yd and Yd = Y − T.
1) Compute C using the given formula and tax: C = 180 + 0.5 Yd, with Yd = Y − T and T = 120. Therefore, C = 180 + 0.5 (Y − 120) = 180 + 0.5Y − 60 = 120 + 0.5Y. This expresses C directly in terms of Y.
2) Sum up autonomous spending: I = 100 and G = 160 are exogenous, so total autonomous spending is 100 + 160 = 260.
3) Total planned expenditure (aggregate demand) as a function of Y is AE = C + I + G = (120 + 0.5Y) + 100 + 160 = 380 + 0.5Y.
Now set equilibrium where output equals aggregate demand: Y = AE = 380 + 0.5Y.
Solving for Y: Y − 0.5Y = 380 → 0.5Y = 380 → Y = 760.
- Option a: 880. This would require a higher multiplier effect or larger autonomous spending, but the derived equation shows Y must satisfy Y = 380 + 0.5Y, so 880 does not satisfy the equilibrium condition.
- Option b: 780. Close to the computed 760, but plugging Y = 780 into the equation yields AE = 380 + 0.5×780 = 380 + 390 = 770, which is not equal to 780, so not equilibrium.
- Option c: 760. This exactly satisfies Y = 380 + 0.5Y, since 0.5×760 = 380 and 380 + 380 = 760, confirming equilibrium occurs at this level of output.
- Option d: 800. If Y = 800, then AE = 380 + 0.5×800 = 380 + 400 = 780, which is less than Y, so the economy would adjust upward or downward? The mismatch shows 800 is not the equilibrium level.
In summary, only Y = 760 balances total spending with output given C, I, G, and T, making 760 the correct equilibrium level of output. All other options fail to satisfy the equilibrium condition Y = C + I + G with the specified components.

Indicate the equilibrium level of output in an economy where: C = 180 + 0.5 Yd I = 100 G = 160 T = 120

View Explanation

Log in for full answers

Similar Questions

Consider a simple Keynesian economy described by the following equations: What is the equilibrium level of output in this economy?

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?

Indicate the equilibrium level of output in an economy where: C = 180 + 0.5 Yd I = 100 G = 160 T = 120

Indicate the equilibrium level of output in an economy where: C = 180 + 0.5 Yd I = 100 G = 160 T = 120

Consider a simple Keynesian economy described by the following equations: 𝐶 = 1800 + 0.6 ( 𝑌 − 𝑇 ) 𝐼 = 900 𝑇 = 100 𝐺 = 100 𝑋 = 50 What is the equilibrium level of output in this economy?

In a consumer society, many adults channel creativity into buying things

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler