Question

n the New Keynesian model, suppose that in the short run the central bank cannot observe

aggregate output or the shocks that hit the economy. However, the central bank would like to come

as close as possible to economic efficiency. That is, ideally the central bank would like the output

gap to be zero. Suppose initially that the economy is in equilibrium with a zero output gap.

(a) Suppose that there is a shift in money demand. That is, the quantity of money demanded

increases for each interest rate and level of real income. How well does the central bank perform

in relative to its goal? Explain using diagrams.

(b) Suppose that firms expect total factor productivity to increase in the future. Repeat part

(a).

(c) Suppose that total factor productivity increases in the current period. Repeat part (a).

(d) Explain any differences in your results in parts (a)-(c), and explain what this implies about

the wisdom of following an interest rate rule for the central bank

Answer 1

a). we can analyses all these possibilities through the AD-AS model. So, if “the demand for money” increases given the “i” and “Y”, => the equilibrium rate of interest will increase, => “investment” will decrease, => “AD” will shift to left side given “P”. So, the new equilibrium is at “E2” at this new equilibrium “Y” reduce to “Y2 < Y1” it create output gap. So to reduce the output gap the central bank must increase the money supply ,=> the equilibrium rate of interest rate will further fall to initial level => “I” further increase, => “AD” will further shift to “AD1”, => “P” and “Y” both increases to it initial level.

Consider the following fig.

b).

Suppose that the initial equilibrium is at “E1” where “Y=Y1” at its natural level. Now, let’s assume that there is an expectation that TFP will increase in future. So, if TFA will increase => LRAS as well as SRAS will shift in the right side leads to increase in “Y” and decrease in “P”. Here there is an expectation that TFP will increase in future, => LRAS will not shift rather people start forming their expectation accordingly, => SRAS will shift down ward, => the new equilibrium is at “E2”, where Y=Y2 > Y1, => there is an output gap. So, here to reduce output gap the central bank should take contractionary moneytary policy, => as the money supply decreases = the equilibrium “i” will increases, => “Investment will reduce, => AD will shift left side in such a way that at the new equilibrium “E3” Y=Y1, where output gap is “0”.   

Consider the following fig.

c).

now, assume that TFA increases => LRAS and SRAS will shift to the right side, => the full employment level of “Y=Y3” now. So, given the AD1 the new equilibrium is “E2” the intersection of “AD1” and “AS2”, here equilibrium Y is Y2 < Y3, => there is an output gap. So, here no reduce the output gap central bank should increase money supply, => the equilibrium “i” will decrease => “I” will increases, => AD will shift to the right side, => the new equilibrium is at “E3” where Y=Y3.

Consider the following fig.

d).

So, if we compare all these cases, we can see that in the 1st case there were "negative output gap" as the full employment level of "Y" is more than actual "Y", in the 2nd case there were "positive output gap" and in the 3rd case there were "negative output gap", => if there is an "positive output gap" (the difference between current and potential output = Yi - Y), the central bank should take contractionary moneytary policy, => “i” will increase, => “I” will decrease, =>AD will reduce, => the economy will come back to the full employment level of output. Similarly if there is a negative output gap the central bank should do totally opposite