Can someone just look over my algebra?

[maeveoneill]

This is an economics question.. but only relies on basic knowledge of algebra to complete. Only necessary to read the bolded parts.
Thanks in advance for your help.

Suppose that for Ecoland desired aggregate expenditure can be represented by the function:
AE= 0.8Y + 6000/P, where Y is real GDP and P is the price level.

Derive the aggregate demand (AD) function from aggregate expenditure function. Aggregate demand is found where Y=AE=Yad

SO subsituting Yad for AE and Y in the aggregate expenditure function I have:
Yad = 0.8Yad + 6000/P
0.2Yad = 6000/ P
Yad = 30000/ P.......is the algebra here right solving for Yad in terms of P??

Then, suppose the aggregate suply (AS) for Ecoloand can be represented by the function Yas = (7500P) x T, where T represents the state of technology. Solve for the equilibrium value of real GDP and the price level in terms of the stae of technology, T. So here we must find P and Y as functions of T when Yad= Yas

If my previous work is correct I have:
Yad = Yas
3000/P = 7500P x T.... and then I'm stuck, how can I solve for P???

 

[tutor_joel]

This is an economics question.. but only relies on basic knowledge of algebra to complete. Only necessary to read the bolded parts.
Thanks in advance for your help.

Suppose that for Ecoland desired aggregate expenditure can be represented by the function:
AE= 0.8Y + 6000/P, where Y is real GDP and P is the price level.

Derive the aggregate demand (AD) function from aggregate expenditure function. Aggregate demand is found where Y=AE=Yad

SO subsituting Yad for AE and Y in the aggregate expenditure function I have:
Yad = 0.8Yad + 6000/P
0.2Yad = 6000/ P
Yad = 30000/ P.......is the algebra here right solving for Yad in terms of P?? Looks Good

Then, suppose the aggregate suply (AS) for Ecoloand can be represented by the function Yas = (7500P) x T, where T represents the state of technology. Solve for the equilibrium value of real GDP and the price level in terms of the stae of technology, T. So here we must find P and Y as functions of T when Yad= Yas

If my previous work is correct I have:
Yad = Yas
3000/P = 7500P x T.... and then I'm stuck, how can I solve for P??? Looks like you're missing a zero in the 30,000/P here. Other than that it's correct

Now, to solve for P, multiply through by P and divide by 7500T to yield...

P^2 = 30000/(7500T) and then

\(\displaystyle P = \sqrt{4/T}\)