Question

Find a numerical equation relating planned aggregate expenditure to output and to the real interest rate. [i.e. write down the PAE equation]

Answer 1

Answer:

The answer is "0.12".

Explanation:

In the given question, some of the information missing. so, the missing information and its solution can be defined as follows:  

Missing information:

$C=14,400+0.75(Y-T)-50,000r\\I^P=7,000-24,000r\\G=8,500\\NX=2,000\\T=9,000\\Y^d=65,080$

Formula:

$\bold{PAE = C + I + G + NX}$

solution:

$\to PAE = 14400 + 0.75 \times (Y - 9000) -50000r + 7000 - 24000r+ 10500$

             $= 14400 + 0.75Y - 6750 -50000r + 7000 - 24000r+ 10500\\\\= 25150 -74000r + 0.75Y$

Calculating the value of r:

let $Y = Y^d = PAE$

  $\to 65080 = 25150 - 74000r + 0.75 \times 65080\\\\ \to 65080 = 25150 - 74000r + 48,810 \\\\\to 74000r= 25150 + 48,810 - 65,080\\\\\to 74000r= 8,880\\\\\to r =\frac{8,880}{74000} \\\\\to r= 0.12$