The following equations describe an economy. (Think ofC,I,G, etc., as being measured in billions andias a percentage; a 5 percent interest rate impliesi=5.) \[ \begin{aligned} C & =0.8(1-t) Y \\ t & =0.25 \\ I & =900-50 i \\ \bar{G} & =800 \\ L & =0.25 Y-62.5 i \\ \bar{M} / \bar{P} & =500 \end{aligned} \] a. What is the equation that describes theIScurve? b. What is the general definition of theIScurve? c. What is the equation that describes theLMcurve? d. What is the general definition of theLMcurve? e. What are the equilibrium levels of income and the interest rate?

a. The IS curve is derived from the equilibrium condition in the goods market, which is Y = C + I + G. Substituting the given equations into this condition, we get:

Y = 0.8(1-0.25)Y + 900 - 50i + 800

Solving for Y as a function of i gives the IS curve.

b. The IS curve represents all combinations of the interest rate and income level at which the goods market is in equilibrium, i.e., where total spending (consumption + investment + government spending) equals total output (income).

c. The LM curve is derived from the equilibrium condition in the money market, which is L = M/P. Substituting the given equations into this condition, we get:

0.25Y - 62.5i = 500

Solving for Y as a function of i gives the LM curve.

d. The LM curve represents all combinations of the interest rate and income level at which the money market is in equilibrium, i.e., where the demand for money equals the supply of money.

e. The equilibrium levels of income and the interest rate are found by solving the IS and LM equations simultaneously. This gives the values of Y and i at which both the goods market and the money market are in equilibrium.