TOPIC: Utility Functions & Calculating Individual Demands Carol (consumer) has preferences over two goods, Dumplings and Eggs In what follows you should use mc to denote the income of Carol and p; for j = D, E to denote the prices of each of the two goods. Similarly, dc and ec denote the consumption of dumplings and eggs respectively N=3 FOR ALL QUESTIONS 4. [14 points] Carol has very weird preferences. She only cares about quantity. When evaluating a bundle, Carol only looks at the highest amount of a good she can consume in each bundle, regardless of whether it is of eggs or dumplings. She is indifferent between two bundles only when the largest consumption of a good within each bundle is the same across bundles. So, for instance, if a bundle offers 5 eggs and 1 dumpling she finds that bundle indifferent to a bundle offering 4 eggs and 5 dumplings. These preferences are transitive. But are they monotone? And convex? 5. (14 points) Find a utility function representing Carol's preferences and find her cor- responding demands of dumplings and eggs as a function of her income mc and the prices of the two goods (which are again pd and pE)