Equilibrium in the goods market is Y*=(a+b-B_o*r+G)/1-a_o); the gradient is -B_o/1-a₀

Equilibrium in the money market is r*= (M₀+mY-M_s)/d; the gradient is m/d

1. How many combinations of output and the interest rate (Y, r) put the goods market in equilibrium?

2. How many combinations of (Y, r) put the money market in equilibrium?

3. How many combinations of (Y, r) put both in equilibrium?

4. Using your answers from above, represent both the goods and money market in Ax = d form where x is the column vector [Y, r].

5. Using linear algebra solve for equilibrium Y and r.