Textbook:

https://mjo.osborne.economics.utoronto.ca/index.php/tutorial/index/1/toc

Hints: a To nd the maximum, use rst order conditions. a An interior stationary point will be a global maximum if the flmction is concave. Question 4 Suppose you are an executive at Yamaha. You are in charge of the company's two most wellknown products: motorcycles and pianos (M and P). Your prot function is the following: Prot = H(qM, qP) = FMQM + PPQP C(QM: 9P) where 10M and pp are the price you sell motorcycles and pianos for, respec tively. Further, C(qM, qp) is the function that maps motorcycles and pianos into a cost. The cost is given by: C(qM, (11:) = q?\" + q? - 4(1qu where the last term represents some costs savings where we are able to use some inputs in the manufacture of both. Assume that the demand functions are given by: 1 QM=23PM 1 GP=12pp a) As the executive, you want to set quantities of output for motorcycles and pianos to maximize prots. Write down the maximization problem. Hint: solve the demand flmctions for price rst. b) Is this maximization problem concave? c) Take rst-order conditions with respect to your two variables and solve for QM and (u (the protmaximizing quantities of motorcycles and pianos). Assume qM and 13;: were denoted in millions, so multiply your answer by 1,000,000