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What is the Expected Value of Perfect information on the payoff of the second investment?

The following description will be used in questions 2a through 2e and in bonus II.   A firm produces x according to the cost function c(x)=20x+25. The demand for x is represented by the inverse price demand curve p=A-bx, where p is the price faced by consumers and A and b are positive numbers.

Assume A=100 and b=2. Find the monopolist’s optimal price and quantity.

Now assume that instead of a monopoly x is produced in a perfectly competitive market. Write the profit maximization problem for a competitive firm in this market. Explain how this problem differs from 2a. 

Why is it important to study production functions such as f1 and f2?

After solving 2d, you can find that the market will offer 40 units of x at a price of 20. As expected, the competitive market can offer x at a lower price than the monopoly. Calculate the dead weight loss from the monopoly.

Now assume that instead of a monopoly x is produced in a perfectly competitive market. Write the profit maximization problem for a competitive firm in this market. Explain how this problem differs from 2a. 

Write down the Lagrangian. (Use L to represent the Lagrangian and m for the multiplier; if you need more multipliers label them as m1, m2, m3, … etc.) 

Write down the complementary slackness conditions. 

Write down the complementary slackness conditions.