Reference no: EM133710933

Question: Consider Pei-Qi's utility function. Suppose it has this particular form: U(l, C) = ln(C) η ln(l), η > 0. where l = h - N, N is labor effort/hours, and total labor endowment is h ≡ 1. We restrict her possible choice over (l, C) to the subset X of the two dimensional plane R 2 , where X = {(l, C) : 0 < l ≤ 1, 0 < C < ∞}. At this stage, we don't presume knowledge of calculus, but we can still derive a concrete example of Pei-Qi's demand curves. (Demand for what?) By a sleight of our calculus hand, we can show that Pei-Qi's marginal utility of consumption is given by the function 1/C. Likewise, her marginal utility of leisure is 1/l, or equivalently, 1/(1 - N). 1. Given Pei-Qi's preferences, her internal or preference-defined rate of exchange (or marginal rate of substitution) between leisure and consumption-i.e., the slope of her indifference curve in (l, C)-space-is given by the (negative of) the ratio of her marginal utility of leisure to her marginal utility of consumption. Write this down using the symbols/notation above. What is the slope of her budget line in (l, C)-space?