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Optimum Price and Output Levels in Profit Maximization

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You have an exclusive contract with Major League Baseball to manufacture Dodgers baseball jerseys and sell them in two markets: Los Angeles and Brooklyn. You produce all the jerseys in a single factory located in Seattle. Your total cost function associated with producing the baseball jerseys is c(Q)=Q2+400 where q is the total amount of jerseys you produce. The inverse demand function for your jerseys in Los Angeles is PLA(QLA)=60-QLA where qLA is the quantity of jerseys sold in Los Angeles. The inverse demand function in Brooklyn is PB(QB)=40-2QB. Assume there is no transportation costs.

How many baseball jerseys will you sell in Los Angeles and how many in Brooklyn? What will be the price of your jersey in Los Angeles and what will be the price in Brooklyn? What will be your total profits?

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Solution Summary

Solution describes the steps to calculate optimal output and price levels for two market segments with the help of given cost and demand functions.

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Solution:

Total jerseys produced =QLA+QB
Total Cost=TC=Q^2+400
TC=(QLA+QB)^2+400

Inverse demand function for Jerseys sold in Los Angeles is given by
PLA(QLA)=60-QLA

Total Revenue for Jerseys sold in Los Angeles is
TR(LA)=PLA*QLA=(60-QLA)*(QLA)=60QLA-QLA^2

Marginal Revenue for Jerseys sold in Los Angeles will be
MR(LA)=dTR(LA)/dQLA=60-2QLA

Marginal ...

Solution provided by:
Lokesh Jain, MSc
Education
  • BEng (Hons) , Birla Institute of Technology and Science, India
  • MSc (Hons) , Birla Institute of Technology and Science, India
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