If the planned aggregate expenditure (PAE) is given by the equation PAE = [1010 –1000r] + 0.8Y and the real interest rate is 5%, what would be the short-run equilibrium output (PAE = Y)?Group of answer choicesY = 2347Y = 3600Y = 8687Y = 4800
Question
If the planned aggregate expenditure (PAE) is given by the equation PAE = [1010 –1000r] + 0.8Y and the real interest rate is 5%, what would be the short-run equilibrium output (PAE = Y)?Group of answer choicesY = 2347Y = 3600Y = 8687Y = 4800
Solution
First, let's substitute the given real interest rate into the PAE equation:
PAE = [1010 - 1000*0.05] + 0.8Y PAE = [1010 - 50] + 0.8Y PAE = 960 + 0.8Y
In the short-run equilibrium, PAE equals Y. So, we can set up the following equation:
960 + 0.8Y = Y
To solve for Y, we can subtract 0.8Y from both sides of the equation:
960 = 0.2Y
Then, divide both sides by 0.2 to solve for Y:
Y = 960 / 0.2 Y = 4800
So, the short-run equilibrium output is Y = 4800.
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