Pergunta
![Goods Market: C=200+0.5(Y-T);I=200-
1000r
G=250;T=200
Question:
Derive the IS relation (i.e. an equation
with Y on one side and everything
else on the other)](https://static.questionai.br.com/resource%2Fqaiseoimg%2F202501%2Fgoods-market-c20005yti2001000rg250t200questionderive-tqZocq4cxK00.jpg?x-oss-process=image/resize,w_558,h_500/quality,q_35/format,webp)
Goods Market: C=200+0.5(Y-T);I=200- 1000r G=250;T=200 Question: Derive the IS relation (i.e. an equation with Y on one side and everything else on the other)
Solução
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Júlia BeatrizMestre · Tutor por 5 anos
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To derive the IS relation, we need to find the equilibrium level of output (Y) where the goods market is in equilibrium. In other words, we need to find the level of output where aggregate demand (AD) equals aggregate supply (AS).
The aggregate demand is the sum of consumption (C), investment (I), and government spending (G). The aggregate supply is equal to the level of output (Y).
Given the information provided:
C = 200 + 0.5(Y - T)
I = 200 - 1000r
G = 250
T = 200
We can write the aggregate demand as:
AD = C + I + G
Substituting the given equations for C and I, we get:
AD = (200 + 0.5(Y - 200)) + (200 - 1000r) + 250
Simplifying the equation, we have:
AD = 200 + 0.5Y - 100 + 200 - 1000r + 250
AD = 0.5Y - 1000r + 350
Now, we can set the aggregate demand equal to the aggregate supply (Y) to find the equilibrium level of output:
Y = 0.5Y - 1000r + 350
To solve for Y, we can rearrange the equation:
0.5Y - Y = -1000r + 350
-0.5Y = -1000r + 350
Y = 2000r - 700
Therefore, the IS relation is:
Y = 2000r - 700
This equation represents the equilibrium level of output (Y) in the goods market, where aggregate demand equals aggregate supply.
The aggregate demand is the sum of consumption (C), investment (I), and government spending (G). The aggregate supply is equal to the level of output (Y).
Given the information provided:
C = 200 + 0.5(Y - T)
I = 200 - 1000r
G = 250
T = 200
We can write the aggregate demand as:
AD = C + I + G
Substituting the given equations for C and I, we get:
AD = (200 + 0.5(Y - 200)) + (200 - 1000r) + 250
Simplifying the equation, we have:
AD = 200 + 0.5Y - 100 + 200 - 1000r + 250
AD = 0.5Y - 1000r + 350
Now, we can set the aggregate demand equal to the aggregate supply (Y) to find the equilibrium level of output:
Y = 0.5Y - 1000r + 350
To solve for Y, we can rearrange the equation:
0.5Y - Y = -1000r + 350
-0.5Y = -1000r + 350
Y = 2000r - 700
Therefore, the IS relation is:
Y = 2000r - 700
This equation represents the equilibrium level of output (Y) in the goods market, where aggregate demand equals aggregate supply.
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