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)?

Question

BlackTom AI · Accepted Answer

The question asks for the short-run equilibrium output where planned aggregate expenditure (PAE) equals output Y, given PAE = [1010 – 1000r] + 0.8Y and r = 5%. 
First, substitute the real interest rate into the PAE expression: 1010 – 1000r becomes 1010 – 1000(0.05) = 1010 – 50 = 960. So PAE = 960 + 0.8Y.
Next, set PAE equal to Y for equilibrium: Y = 960 + 0.8Y. 
Then collect like terms by subtracting 0.8Y from both sides: 0.2Y = 960. 
Solving for Y gives Y = 960 / 0.2 = 4800. 
Now, regarding the answer choices: the provided data show an answer of Y = 4800, but there are no listed answer options to review. 
Understanding the steps helps verify the result: the linear relationship PAE = 960 + 0.8Y crosses the 45-degree line (Y = PAE) where the slope difference 1 − 0.8 = 0.2 yields the 960 intercept translated into Y = 4800. 
If you expected multiple-choice options, ensure you include them so you can compare each alternative against the derived equilibrium condition. 
In summary, plugging r = 5% into PAE, setting PAE = Y, and solving yields Y = 4800, which matches the stated answer.

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)?单项选择题

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