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4. 10 pts. A monopolists inverse demand function is P 500-0.5Q. The company produces out at two plants; the cost of producing at plant l İs C(QI)-45Q1+4Q12. The cost of producing output at plant 2 is given by C(Q2) 452Q22

a. Solve for the optimal output to produce at each plant (Q1*, Q2*).

b. Given this output, what is the firm’s price and maximum profit?

c. Suppose the monopolist is now facing a capacity constraints at plant 2. Due to a labor dispute, there are only enough labor hours to produce 70 units at plant 2. How will this constraint impact the firm’s decision of Q1*, Q2*, price and profit?

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