Question

whole question: Just answer as many as possible, dont have to be 100%
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) = 120 +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 (G)? (c) Use your answer to explain why each consumer's demand for beans is B* = po (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? An impending snow storm leads people to stock up on beans. Suppose all 9,000 consumers in this small town try to buy beans in the same week. (i) What is the new market demand curve for beans? 6) What is the competitive equilibrium price PB? Do markets clear at this price? (k) Solve for the new optimal bundle and utility level for each consumer after the price change in a competitive equilibrium.

Answer 1

Due to presence of HOMEWORKLIB POLICY, I am answering first 4 parts.

1.

a.

We have:

b.

We have:

Utility function:

c.

Deriving demand for B:

Optimal condition:

MRS = Price ratio

So, we have:

We get:

d.

Demand for beans is not dependent is not dependent on income level(I) implying it is neither normal nor inferior.

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