3. (a) If each consumer's utility function is continuous, strongly increasing, and strictly quasi concave on R and if the aggregate endowment of each good is strictly positive, then show that there exits one price vector, p* » 0, such that z(p*) = 0. (b) Suppose that 10 people live on a street and each of them is willing to pay $2 for each extra street light, regardless of the number of street lights provided. If the cost of providing street lights is given by C(x) = x², what is the Pareto efficient number of street lights to provide?

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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3. (a) If each consumer's utility function is continuous, strongly increasing, and strictly
quasi concave on Rị and if the aggregate endowment of each good is strictly positive,
then show that there exits one price vector, p* » 0, such that z(p*) = 0.
(b) Suppose that 10 people live on a street and each of them is willing to pay $2 for each
extra street light, regardless of the number of street lights provided. If the cost of
providing street lights is given by C(x) = x², what is the Pareto efficient number of
street lights to provide?
Transcribed Image Text:3. (a) If each consumer's utility function is continuous, strongly increasing, and strictly quasi concave on Rị and if the aggregate endowment of each good is strictly positive, then show that there exits one price vector, p* » 0, such that z(p*) = 0. (b) Suppose that 10 people live on a street and each of them is willing to pay $2 for each extra street light, regardless of the number of street lights provided. If the cost of providing street lights is given by C(x) = x², what is the Pareto efficient number of street lights to provide?
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