Consider a local market where there are two local firms, A and B with the following cost functions producing homogenous good: CA=q₁² +50q4-98² CB=2q8² +70qB+0.25q² where q and qв represent the production levels of firm A and firm B, respectively. The market price of the good produced by two firms is equal to 150. Furthermore, suppose that the two firms act as price-takers (because firms from other locations also serve it). a) Briefly describe the relationship between the two firms (Hint: study the cost structure). b) Find the production levels and the profits of the two firms, assuming that they operate independently.

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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Consider a local market where there are two local firms, A and B with the following cost functions
producing homogenous good:
CA=qA² +509A-9B²
CB= 2qB² + 70qB+0.25qA²
where q4 and qв represent the production levels of firm A and firm B, respectively. The market price
of the good produced by two firms is equal to 150. Furthermore, suppose that the two firms act as
price-takers (because firms from other locations also serve it).
a) Briefly describe the relationship between the two firms (Hint: study the cost structure).
b) Find the production levels and the profits of the two firms, assuming that they operate
independently.
c) Determine the production levels and the profits of the two firms, corresponding to a Pareto-
efficient equilibrium in the absence of government intervention. Compare these results with
those obtained in the previous point.
d) Using the quantities calculated in point c) find the level of taxes and subsidies which would
allow to reach the Pareto efficient equilibrium, in case the two firms operate independently.
Assume that the government can introduce a tax t on each unit of output of firm A, and a
subsidy s on each unit of output of firm B.
Transcribed Image Text:Consider a local market where there are two local firms, A and B with the following cost functions producing homogenous good: CA=qA² +509A-9B² CB= 2qB² + 70qB+0.25qA² where q4 and qв represent the production levels of firm A and firm B, respectively. The market price of the good produced by two firms is equal to 150. Furthermore, suppose that the two firms act as price-takers (because firms from other locations also serve it). a) Briefly describe the relationship between the two firms (Hint: study the cost structure). b) Find the production levels and the profits of the two firms, assuming that they operate independently. c) Determine the production levels and the profits of the two firms, corresponding to a Pareto- efficient equilibrium in the absence of government intervention. Compare these results with those obtained in the previous point. d) Using the quantities calculated in point c) find the level of taxes and subsidies which would allow to reach the Pareto efficient equilibrium, in case the two firms operate independently. Assume that the government can introduce a tax t on each unit of output of firm A, and a subsidy s on each unit of output of firm B.
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