1. There is a company that seeks to maximize its benefits in a perfectly competitive market, said company has to accept the price of the good that is equal to P = $250. The company has 4 machines (K=4) and the intensity with which it will use capital and labor will be (1/4) each. What is the amount of labor that the producer will need to maximize his profits?

Show that profit is being maximized through the second derivative

What are the benefits of the company?

2. Optimal choice of both factors of production in the long run. Consider a firm that seeks to maximize its profits . The firm must choose how many workers it needs to produce q units of goods and make a profit. The price of the good is P, and its output is generated from its function shown below where < 1 and < 1. The cost of capital is r and the cost of labor is w. The price of the good is $400 the cost of capital, r is $2 The cost of labor, w is $20 Alpha equals 1/3 Beta equals 1/3 A) Find the MTRS of capital in terms of labor

What is the optimal number of workers?

What is the optimal amount of capital?