Part C. Consider an economy consumes food (F) and shelter (S). use the following utility function. Where applicable, round your answers to the nearest one hundredth (1.01, not 1.0 or 1.011). U = U(F, S) = 0.4lnF + S C1) What is the marginal utility of shelter (MUS)? C2) What is the partial derivative if MUs with respect to shelter? C3) This utility function exhibits Explain your answer relating to the second derivative. C4) Explain, in your own words, the intuitive meaning of what you found in C2 and C3. CS) What is the marginal rate of substitution (MRS) for this utility function? Also evaluate the MRS when F-1 and S-2? Explain the meaning of the marginal rate of substitution you found? C6) Suppose Alice and Bob each have 1,000 units of food and shelter but different marginal rates of substitution: Alice: OF as = -3 == marginal utility shelter. (diminishing, constant, increasing). OF Bob: = -1 as Suppose Alice offers Bob 1 unit of food in exchange for shelter. If Bob gives Alice between and 1 units of shelter, then the trade is mutually beneficial. Justify your answer. C7) Suppose an economy consists of just two people: Alice and Bob. Alice and Bob are thinking about how to allocate resources towards food and shelter. In this economy, there are just four ways to organize resources: Option A: A little food and a little shelter Option B: A lot of food and a little shelter Option C: A little food and a lot of shelter Option D: A medium amount of both food and shelter Option A B C D Alice 1 100 30 60 Bob 10 300 1,000 600 The table above gives the utility of Alice and Bob under each option. For example, under option A (second column from left), Alice has a utility of 1 and Bob has a utility of 10. C7.1) Notice that Bob's utility is always higher than Alice's. What does this tell us about their relative levels of happiness? C7.2) Which option(s) are pareto inefficient? Justify your answer. C7.3) Which option does economic theory say is the best one? Justify your answer.