An economy is described by the following relationships:

C = c_o + c₁Y_D – c₂r

Y_D = (1 – t)Y

I = I_o

L = L_o + m₁Y – m₂r

M^S = M

Where C is consumption, Y is income, I is investment, r is the rate of interest L is the real demand for money and M^S is the nominal supply of money (hence, defining P as the price level,  M^S/P is the real supply of money).  Y_D is disposable income and t is the rate at which income is taxed.

Explain why consumption is negatively related to the rate of interest.

1. Derive the equations for the IS and LM curves that describe this economy. For a given price level, P, what would be the equilibrium level of income and the rate of interest?

1. Still for a given level of P, what would be the effect of an increase in the rate of taxation t on the equilibrium rate of interest? Explain why we have such an effect (i.e. what happens in the product market and in the money market?).

1. Obtain the macroeconomic demand schedule for this economy? How does this schedule shift if M^S decreases? Why?