申論題

3. Goods I and 2 are available at prices (in dollars) of p₁ per unit of good 1 and p₂ per unit of good 2. A utility function U(x₁, x₂) is a function representing the utility or beneit fo consuming x_j, units of good j. The marginal utility of the jth good is , the rate of increase in utility per unit increase in the jth good. Prove the following law of economics: Given a budget of L dollars, utility is maximized at the consumption level (a,b) where the ratio of marginal utility is equal to the ratio of prices: