Here's how to calculate the equilibrium Y and r: Step 1: Derive the IS curve (Goods Market Equilibrium) The goods market equilibrium is given by the equation: $$Y = C + I + G$$ We are given: $C = 1000 + 0.75 Y^d$ $I = 1000 - 100r$ $G = 100$ $T = 0.2Y$ First, calculate disposable income ($Y^d$): $$Y^d = Y - T = Y - 0.2Y = 0.8Y$$ Substitute $Y^d$ into the consumption function: $$C = 1000 + 0.75(0.8Y) = 1000 + 0.6Y$$ Now substitute C, I, and G into the goods market equilibrium equation: $$Y = (1000 + 0.6Y) + (1000 - 100r) + 100$$ $$Y = 2100 + 0.6Y - 100r$$ Rearrange to solve for Y: $$Y - 0.6Y = 2100 - 100r$$ $$0.4Y = 2100 - 100r$$ $$Y = \frac{2100}{0.4} - \frac{100}{0.4}r$$ $$Y = 5250 - 250r \quad \text{(IS curve)}$$ Step 2: Derive the LM curve (Money Market Equilibrium) The money market equilibrium is given by the equation: $$M_s = L_1 + L_2$$ We are given: $L_1 = Y$ $L_2 = 1 - 1000r$ $M_s = 2751$ (Assuming the 'I' is a typo and $M_s = 2751$) Substitute $L_1$, $L_2$, and $M_s$ into the money market equilibrium equation: $$2751 = Y + (1 - 1000r)$$ $$2751 = Y + 1 - 1000r$$ Rearrange to solve for Y: $$Y = 2751 - 1 + 1000r$$ $$Y = 2750 + 1000r \quad \text{(LM curve)}$$ Step 3: Solve for Equilibrium Y and r Now we have a system of two equations: 1) $Y = 5250 - 250r$ (IS curve) 2) $Y = 2750 + 1000r$ (LM curve) Set the two expressions for Y equal to each other to find r: $$5250 - 250r = 2750 + 1000r$$ $$5250 - 2750 = 1000r + 250r$$ $$2500 = 1250r$$ $$r = \frac{2500}{1250}$$ $$r = 2$$ Substitute the equilibrium value of r back into either the IS or LM equation to find Y. Using the IS curve: $$Y = 5250 - 250(2)$$ $$Y = 5250 - 500$$ $$Y = 4750$$ The equilibrium values are: Equilibrium interest rate $r = \boxed{\text{2}}$ Equilibrium output $Y = \boxed{\text{4750}}$