1. **Stating the problem:** We have a demand function for good X: $$X = 20 + MPx^{-2}$$ where $M$ is income, $P_x$ is the price of good X, and $X$ is quantity demanded. Originally, income $M=200$, price $P_x=5$. The price falls to $P_x=4$. We need to find the substitution effect, income effect, and total price effect. 2. **Understanding the effects:** - Total price effect = change in quantity demanded due to price change. - Substitution effect = change in quantity demanded holding utility constant (compensated demand). - Income effect = change in quantity demanded due to change in real income after price change. 3. **Calculate original quantity demanded:** $$X_0 = 20 + \frac{M}{P_x^2} = 20 + \frac{200}{5^2} = 20 + \frac{200}{25} = 20 + 8 = 28$$ 4. **Calculate new quantity demanded after price change:** $$X_1 = 20 + \frac{200}{4^2} = 20 + \frac{200}{16} = 20 + 12.5 = 32.5$$ 5. **Calculate compensated income $M_c$ to keep utility constant:** Utility is constant when $$X = X_0 = 28$$. Solve for $M_c$: $$28 = 20 + \frac{M_c}{4^2} \Rightarrow 28 - 20 = \frac{M_c}{16} \Rightarrow 8 = \frac{M_c}{16} \Rightarrow M_c = 128$$ 6. **Calculate quantity demanded at new price with compensated income (substitution effect):** $$X_c = 20 + \frac{128}{4^2} = 20 + \frac{128}{16} = 20 + 8 = 28$$ 7. **Calculate effects:** - Substitution effect = $$X_c - X_0 = 28 - 28 = 0$$ - Income effect = $$X_1 - X_c = 32.5 - 28 = 4.5$$ - Total price effect = $$X_1 - X_0 = 32.5 - 28 = 4.5$$ **Final answer:** - Substitution effect = 0 - Income effect = 4.5 - Total price effect = 4.5