2. Suppose that the utility function U (e,s): =e+4s2 describes Elle's preferences over two goods: Eggo brand waffles (e) and sodas (s). For the following, think of Eggos as the good graphed on the horizontal axis. a. Derive an expression for her marginal utility (Ue) from a small increase in e holding s fixed. Also find the marginal utility for sodas (US). b. What is Elle's marginal rate of substitution (MRS)? Give a brief (2 sentences maximum) intuitive description of what MRS represents. If Elle has 4 units of soda, holding her utility constant, how many units of soda would she be willing to give up in order to get one more unit of Eggos? Find the equation for and graph Elle's indifference curve for a utility level of 40. Be sure to specify at least 3 bundles of goods on the indifference curve. C. d. Which assumption about preferences means that Elle's indifference curve should slope down? Briefly support your answer. e. 1 Give another utility function that represents Elle's preferences just as well as U (e, s) = e + 4s . Show that the formula for MRS for the new utility function ends up being the same as what you found for the original function in part b.