You are the manager of a business in a competitive market and your production technology is described by the total cost function (q) = 150 + 5q +(1/10)q2 In addition, assume the market price is p = 15 dollars.
a) Determine the optimal quantity to produce and compute the profit of your business.
b) Assume you have the opportunity to make an investment which would improve your production technology and would result in the new total cost function given by C(q) = 150 + 5q +(1/20)q2
i) Determine the optimal quantity to produce with the new technology and compute the profit of your business.
ii) Assume the business will operate for only one period, either with the old or the new technology. If the cost of the investment to improve
your technology is 300 dollars, should you make the investment?