Consider that a consumer has the following utility function u(x) = xas xb, where xi denotes...

  

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Consider that a consumer has the following utility function u(x) = xas xb³, where xi denotes the consumption of good i E {a,b}. Let pi denote price of good i. This consumer's income is y. He is the only consumer in the markets. (a) Derive the consumer's Marshallian demand for each good. The fol- lowing equation shows the demand of the consumer for good a, de- noted by xa (p,y). Choose the best alternatives in place of O. xa (p, y) = (b) Consider the market for good a. Assume that there are J identical firms in the good a market. Each firm's cost function is c(q) = 16+q² where a denotes the amount of production. Assume that pb = 1. Compute the short-run market equilibrium in the market for good a. Choose the best alternatives in place of O. The price of good a in the short-run eqm: pa* = = (c) Consider the good a market, and assume the same cost function and pb in the previous question. Compute the long-run market equilib- rium with y = 8000. Choose the best alternatives in place of . The price of good a in the long-run eqm: pa** = 0, The number of firms in the long-run eqm: J* = 0 Consider that a consumer has the following utility function u(x) = xas xb³, where xi denotes the consumption of good i E {a,b}. Let pi denote price of good i. This consumer's income is y. He is the only consumer in the markets. (a) Derive the consumer's Marshallian demand for each good. The fol- lowing equation shows the demand of the consumer for good a, de- noted by xa (p,y). Choose the best alternatives in place of O. xa (p, y) = (b) Consider the market for good a. Assume that there are J identical firms in the good a market. Each firm's cost function is c(q) = 16+q² where a denotes the amount of production. Assume that pb = 1. Compute the short-run market equilibrium in the market for good a. Choose the best alternatives in place of O. The price of good a in the short-run eqm: pa* = = (c) Consider the good a market, and assume the same cost function and pb in the previous question. Compute the long-run market equilib- rium with y = 8000. Choose the best alternatives in place of . The price of good a in the long-run eqm: pa** = 0, The number of firms in the long-run eqm: J* = 0

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To solve the consumers problem and derive the Marshallian demand for each good we must set up and solve the consumers utility maximization problem given by their utility function ux xa23 xb13 subject ... View the full answer