An economy has the following AD and AS (with misperceptions) curves: AD curve: Y

Question

An economy has the following AD and AS (with misperceptions) curves:

AD curve: Y =G+30(M/P) AS curve: Y =Y +10(P -Pe) Suppose initially Y = 500; G = 260 and M = 480:

(a) Suppose that Pe = 60: Show that the equilibrium price level, P=60. What is the level of output, Y ?

(b) Suppose now an unforeseen shock to government expenditure, G; occurs whereby G rises to 420 but Y is una§ected. Show that the new equilibrium price level, P= 72. What is the implied value of Y ? Explain the diference from part a.

(c) Once the public realize what has happened what are the new levels of Y; P and Pe?

(d) Suppose now, though, that in fact the increase in G causes a wealth e§ect which makes people work harder and Y increases to 600. In this case what would be the long-run levels of Y; P and Pe? Explain the diference from part c.

Explanation / Answer

Answer:

AD curve: Y =G+30(M/P)

AS curve: Y = Y +10(P -Pe)

Y = 500;

G = 260

M = 480:

(a) Suppose that Pe = 60: Show that the equilibrium price level, P = 60. What is the level of output, Y?

     Given Pe= 60 and P = 60

Pe= 60 and Setting AD = AS to eliminate Y, Plugging in the values of M and Pe values then we get:

                = 260 + 30(480/P) = 500+10(60 - P)

Plugging in the values of M and Pe values then we get,

                = 260 + 30(480/P) = 500+10(60 - P)

P can't be negative, so the only solution o this equation is P= 60. At this equilibrium P = Pe, so Y = 500, and the economy is at full-employment output.

And also derive this with another way, that is:

Pe= 60 and P = 60

We can substitute Pe and P values into the AS function, then we can get the equilibrium level of output. That is:

                Y = 500 +10(60 - 60)

                Y = 500 + 10 (0)

                Y = 500

    Therefore, the equilibrium quantity or output (Y) is: 500

(b) Suppose now an unforeseen shock to government expenditure, G; occurs whereby G rises to 420 but Y is unaffected. Show that the new equilibrium price level, P = 72. What is the implied value of Y? Explain the difference from part a.

   If G = 420 and P = 72

We can substitute new G value and new P values into the AD function; then we can get the new equilibrium level of output. That is:

                Y = 420 + 30(480/72)

                Y = 420 + 200

                Y = 620

   The increase in the price and government spending leads to increase the quantity or output.

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