You are a monopolist with 2 production facilities. The production costs at the f

Question

You are a monopolist with 2 production facilities. The production costs at the facilities are:

TC1= 10Q1 + Q1^2
TC2= 10Q2 + Q2^2

Demand for your product is P=100-Q

1) What total output (Q1 + Q2) will you produce to maximize profits?
2) Of the total output in part (1), how many units are produced at teh first facility (what is Q1)?
3) Of the total out put in part (1), how many units are produced at the second facility (what is Q2)?
4) What is the market price for your product?
5) What are your profits at the profit maximizing output level

Explanation / Answer

both cost function are same so we can take net total cost function as TC =10Q+Q^2 here MTC =marginal total cost =10+2Q wich must be equal to price for profit maximization hnce 10+2Q =100-Q hence Q =30 hence Q which is equal to Q1+Q2 =30 as cost function is same Q1=Q2 and hence =30/2 =15 price is given by P=100-Q and for Q =30 market price =P =100-30 =70 TC1 =10Q1+Q1^2 =10*15+15^2 =375 ....as Q1 =15 as calculated similarly TC2 =10Q2+Q2^2 =375 rvenue for each =P*Q1 =70*15 =1050 hence profit of each firm =1050-375 =675

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