The equation
𝑌
¯
=
𝐶
(
𝑌
¯
−
𝑇
)
¯
+
𝐼
(
𝑟
)
+
𝐺
¯
may be solved for the equilibrium level of:

Question

The equation 
𝑌
¯
=
𝐶
(
𝑌
¯
−
𝑇
)
¯
+
𝐼
(
𝑟
)
+
𝐺
¯
  may be solved for the equilibrium level of:

BlackTom AI · Accepted Answer

To approach this equation, first recognize that we have an identity for the equilibrium level of output that links planned aggregate spending to the actual economy-wide income.
Option 1: income. This choice is plausible because the left-hand side is a bar Y, which denotes the equilibrium level of income/output, and the right-hand side expresses it as a function of consumption (which depends on income), investment (a function of the interest rate), and government spending. In standard macro models, solving the equilibrium condition yields the level of income that clears the goods market, so income is the endogenous variable determined by the exogenous components C, I(r), and G. 
Option 2: consumption. While consumption C is a component of the right-hand side and depends on income (through a consumption function of the form C = C(Ȳ − T̄)), the equation does not prompt us to solve for C directly; instead C is a function of income, and income is solved to satisfy the identity. Thus consumption is not the primary endogenous unknown being solved for. 
Option 3: government purchases. Government purchases Ḡ appear as an exogenous term in the identity. They influence the level of income, but they are not the variable solved for within this equilibrium condition; rather, they shift the line and determine the resulting income when combined with other components. Therefore, Ḡ is not the endogenous equilibrium variable here. 
Option 4: the interest rate. I(r) represents investment as a function of the interest rate, but r is typically treated as given (or determined in a larger model by monetary policy or IS-LM mechanisms). In the single-equation equilibrium provided, r is not being solved for; instead, it enters the investment term, shaping the level of income indirectly.
In summary, this identity is used to determine the overall level of income/output that equilibrates the economy given consumption behavior, investment sensitivity to the interest rate, and government spending. The endogenous quantity that is solved for is the equilibrium income, while consumption, government purchases, and the interest rate act as inputs or determinants rather than the solved-for variable.

BU.220.610.51.FA25 M2 Practice Quiz

The equation 𝑌 ¯ = 𝐶 ( 𝑌 ¯ − 𝑇 ) ¯ + 𝐼 ( 𝑟 ) + 𝐺 ¯ may be solved for the equilibrium level of:

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