Prof. Jonathan Gruber, The Budget Constraint (3.16) - Calculating Marginal Utility and the MRS in Consumer Choice Theory
So let's say this mathematically. At a point like A you have your marginal utility for pizza is the derivative of the utility function with respect to the number of slices of pizza. It's the marginal utility. It's derivative of the utility function. So it's dU/dp, which is equal to 0.5 times C over square root of P times C. MUp = dU/dp = 0.5 x c / And at point A we had two cookies and five pizzas. At point A, P was five C was two that's true of point A. So we can evaluate the marginal utility. dU/dp, which equals 0.5 times C over square root of P times C. So that's 1 over the square root of 10. That's the marginal utility of the next slice of pizza. The next slice of pizza makes you 1 over square root of 10 happy. Once again, that number is meaningless. So we only care about it in ratios. So we need the ratio. So let's do the marginal utility of cookies. That's dU/dc, which is 0...