Question

1. Consider the market for dried beans in a small town of 9,000 consumers. Let each consumer's preferences over beans (B, in pounds and other goods (G) be given by U(B,G) = 12BŽ +G For the rest of this question, fix the price of other goods at PG = 1 and let each consumer have a total weekly budget of I = 100. (a) Write the budget constraint for a consumer in terms of the price of beans, PB, and any other variables you need. (b) What is the marginal rate of substitution between beans and other goods (6)? (c) Use your answer to explain why each consumer's demand for beans is B* (d) Would you describe beans as a normal good, an inferior good, or neither? Explain. Suppose only 1,000 consumers show up to the store to buy beans in a typical week. Let the weekly supply of beans be perfectly inelastic at 9,000 as stores can't adjust their stock in such a short time period. (e) What is the weekly market demand curve for beans when there are 1,000 consumers? (f) Solve for the market-clearing price of beans. (g) At this price, what is each consumer's optimal bundle? That is, how many pounds of beans does each consumer purchase, and how much do they spend on everything else? (h) What is each consumer's utility in the market equilibrium?

Answer 1

whity : U(8,4)=1284 +9 Lei Seter goods ] Pu=1 ; Income (I) = 100; 9ooo connemers al Budget constrainto - Consumption = Income PBB t pu a sloo Budget mint [BPB + u <loo] ... I by Margind rate of substitution ou = 12(+) B? IB -26 Margind I do rate of I dB substitution L obtimel : | mRsl = 1 bell Indifforine e udget ling ww. bчает 1 d dB" = I o The optional consumption of Bis independent of Income. so, it is neither normal good non infenor 4

D 9000 only too consumer show up weekly supply = 9000 e) weekly market demand cure for beans. ine are e Market market Demand a Demand = fooo B lowo/3 booo R f} market clearing price Market demand z market supply 36000 - goo [2=Pg Consumer's optimal bundle 9) 9 = I PBB* C h) [4= 100 - 219) = 82] money spend on Beans = PzB " = 18 money spend on other goody=f2 utility : 4 (8,4)= 12B² + 4 = 12197²782 = 12 132782 So, di ling is not = 118