Microeconomics 2nd Edition by Douglas Bernheim

Exercise 4

A firm has two production plants. The cost function of plant 1 is C 1 ( Q 1 )= 10 Q 1 + 0.5( Q 1 ) 2 , where Q 1 is the number of units of output produced in plant 1. The cost function of plant 2 is C 2 ( Q 2 ) = 10 Q 2 + 2( Q 2 ) 2 , where Q 2 is the number of units of output produced in plant 2.
a. If the firm wants to produce Q total units of output, what fraction of Q will a cost minimizing firm produce at plant 1
b. What is the firm's total cost as a function of Q
c. Suppose the firm has an avoidable fixed cost of 10. What is its supply function