2. A closed economy can be represented by the following relationships (where C is consumption, Y income, T tax revenue, i the interest rate, I investment, G government spending, ? is the inflation rate and ?* =2% is the targeted inflation rate, Y_n =900 is the natural level of income and i* = 5% is the long term equilibrium interest rate)

(2.1) ?=250+0.6(??)Consumption equation

(2.2) ?=150+0.02?3000? Investment equation

(2.3) ?=200 Government spending

(2.4) ?=0.2?Income Tax equation

(2.5) ?=?^*+0.5(??^*)+ 0.0001(??_?) Monetary policy (MP) equation

(a)Derive an expression for the IS equation for this economy. Use the MP equation to demonstrate that in equilibrium, Y=900 and i=i*, assuming that the inflation rate is at its target of 2%. Graph the two curves and indicate the equilibrium point.

(b)What are the equilibrium values of consumption, investment and the fiscal balance?

(c)What is the effect on Y, i, and tax revenue of increasing government spending? Represent this change in the IS-MP diagram.

(d)How would the model be affected if the tax rate was cut? Represent this change in IS-MP diagram, indicating clearly the reason of the change.

(E) Explain how the conclusions of your analysis in (c) and (d) could be different when prices are allowed to change and aggregate supply is taken into account, distinguishing short term effects (when the AS is flat and price do not move) and medium term effect (when the AS is upward sloping).