See below: An economy has the following AD and AS curves: AD curve: Y = 700 + 40

Question

See below:

An economy has the following AD and AS curves: AD curve: Y = 700 + 40(M/P) AS curve y = y + [10 times (P - P)] Let Y = 1,500 and M = 800. Suppose that Pe = 40. Calculate the equilibrium value of the price level, P. (Round your answer to two decimal places.) Calculate the equilibrium value of output Y. (Round your answer to the nearest whole number.) An unanticipated increase raises the money supply to M = 924. Because this increase in the money supply is unanticipated, P6 remains at 40. Calculate the short - run equilibrium value of the price level P. after this unanticipated increase in money supply. (Round your answer to two decimal places.) Calculate the short - run equilibrium value of output Y; after this unanticipated increase in money supply. (Round your answer to ihe nearest whole number.)

Explanation / Answer

AD Curve: Y = 700 + 40(M/P)

AS Curve: Y = Y(bar) + [10 x (P - Pe)]

Given Y(bar) = 1500, M = 800, and Pe = 40.

Then using the values above in AD and AS curve, we get

AD: Y = 700 + 40(800/P) => Y = 700 + 32000/P

AS: Y = Y(bar) + [10 x (P - Pe)] => Y = 1500 + 10*(P - 40) = 1500 + 10P - 400 => Y = 1100 + 10P

a) At equilibrium, AD = AS

Equaling Y across the above AD and AS equation we get

700 + 32000/P = 1100 + 10P

=>32000/P - 10P = 400

=> 32000 - 10P^2 = 400P

=> P^2 + 40P - 3200 = 0

=> P^2 + 80P - 40P - 3200 = 0

=> P(P + 80) - 40(P + 80) = 0

=> (P+80)(P-40) = 0

=> P = -80 or P = 40

But as prices cannot be negative, we have equilibrium P = 40

Equilibrium Output Y = 1100 + 10P = 1100 + 10*40 = 1100 + 400 = 1500

b) In this case M increases to 924, while all other values remain the same

Using the approach above, we get

AD: Y = 700 + 40(924/P) => Y = 700 + 36960/P

AS: Y = Y(bar) + [10 x (P - Pe)] => Y = 1100 + 10P

At equilibrium, AD = AS

Equaling Y across the above AD and AS equation we get

700 + 36960/P = 1100 + 10P

=>36960/P - 10P = 400

=>36960 - 10P^2 = 400P

=> 3696 - P^2 = 40P

=> P^2 + 40P - 3696 = 0

=> P^2 + 84P - 44P - 3696 = 0

=> (P + 84)(P - 44) = 0

=> P = -84 or P = 44

But as prices cannot be negative, we have equilibrium P (short-run) = 44

Equilibrium output Y (short-run) = 1100 + 10P = 1100 + 10*44 = 1100 + 440 = 1540

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