Problem 4 - Trade and MRS (40 points) Antonio and Kate have preferences over Starbursts and M&Ms (goods 1 and 2, respectively) that are represented by utility functions, WA (21, 202) = 2VX1 + 22 UK (21, X2) = 2V21 + 22 where uA is Antonio's utility function and ux is Kate's utility function. Antonio has an initial endowment of eA = (16, 0) and Kate's initial endowment bundle is ex = (0, 6). 1. Determine Kate and Antonio's respective utility levels if they are to simply consume their initial endowments, uk (ex ) and uA(eA). 2. Determine MRSA (x), that is Antonio's marginal rate of substitution given consumption bun- dle x. Determine MRSA(eA) 3. Determine MRSK (x), that is Kate's marginal rate of substitution given consumption bundle x. Consider a hypothetical endowment bundle ek = (E, B). Determine Kate's marginal rate of substitution in her endowment bundle as MRSK (ek ) = lime- MRSK (ex) - It is ok to state a non-existent limit that increasing or decreasing without bound as either too or -co. 4. Determine the equation for Antonio's indifference curve that runs through his endowment bundle, eA. Draw it. 5. Let us consider if by engaging in trade, Antonio and Kate can improve their outcomes relative to simply consuming their respective endowment bundles. Specifically, taking their endow- ments as their initial conditions, consider a trade where Kate trades with Antonio to receive Starbursts in return for M&M's. To begin with, consider a trade where Kate acquires 4 Starbursts from Antonio. 2 (a) What is the least number of M&M's Antonio will require to be willing to make the trade? For these exercises, assume candy is perfectly divisible. (b) Would Kate be willing to pay this amount of M&M's? What is the most Kate would have been willing to pay