1. Foundations of Demand a. Consider an economy with a continuum of consumers with "unit demand”.Speci?cally, each consumer must decide whether or not to spend moneyto buy a sandwich. Consumer i’s...

1. Foundations of Demand a. Consider an economy with a continuum of consumers with "unit demand”.Speci?cally, each consumer must decide whether or not to spend moneyto buy a sandwich. Consumer i’s utility function is given by 17, — p, if buys one sandwichui = l 0, if does not buy,where p denotes the price of sandwiches, and consumers’ valuations forthe sandwiches, 12,-, are uniformly distributed between 0 RMB and 10RMB. Express both algebraically and graphically (i) the aggregatedemand for sandwiches and (ii) the aggregate inverse demand forsandwiches. b. Now suppose, instead, that the economy has two consumers. Each mustdecide on a quantity of sandwiches to buy. (Assume that it is possible toconsume any nonnegative, real number of sandwiches]. Both consumershave the same utility function, u = 1203) — pq, where q denotes thequantity purchased and 1203), the gross surplus derived from consumingsandwiches, is given by the function 2 110q — 10g , q E [0,5]17(61) = 5 — >12.2’ q / i. Graph the gross surplus function of an individual consumer.ii. Derive an individual consumer’s demand function, and express itboth algebraically and graphicallyiii. Express both algebraically and graphically the aggregate demandfor sandwiches and the aggregate inverse demand for sandwiches.c. In view of your answers to (a] and (b), brie?y comment on what thebene?ts might or might not be to doing analysis of markets in a way thatgoes “beyond aggregate demand curves” to specify "micro-foundations”,such the utility functions of individual consumers.