Consider an economy in which the price level does not change over time and so the real interest rate is equal to the nominal interest rate

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Consider an economy in which the price level does not change over time and so the real interest rate is equal to the nominal interest rate. The demand for goods is given by:

Z = a₀ + a₁?Y - a₂?i

while the demand for real money balances is given by:

(M/P)^d = b₁?Y - b₂?i.

 

The supply of real money balances is given by M*.

The parameters of the model, (a₀, a₁, a₂, b₁, b₂, M*), are all assumed to be positive.

 

(a)   Find the equilibrium level of output for this economy. Hint: For the IS curve, solve for i as a function of Y (taking into account that Z = Y), and for the LM curve, solve for i as a function of Y (and M*). From these two equations, solve for the equilibrium value of Y (where the IS and LM curves intersect). You should end up with Y as a function of all of the parameters, (a₀, a₁, a₂, b₁, b₂, M*).

 

(b)  Suppose the government increases its spending by 1. Which of the parameters of the model, (a₀, a₁, a₂, b₁, b₂, M*), will change and why?

 

(c)   In (b), by how much does equilibrium output increase?

 

(d)  The IS multiplier is given by . Show that the multiplier in (c) is less than this and provide an intuitive explanation as to why this is.