1. Suppose you are told that the production function for widgets is given by the following equation where Q is the quantity of widgets, K is the number of units of capital used in producing widgets, and L is the number of units of labor used in producing widgets:

Q = 4K^1/2L^1/2

You are also told that total cost for this firm can be found by using the following equation where TC is total cost, P_k is the price per unit of capital, and P_l is the price per unit of labor:

TC = P_k K + P_l L

a. Using this information, fill out the following table depicting the production function and the cost functions for this firm. Make sure you provide the units of measurement in your answers. If necessary, round your answers to the nearest hundredth.

b. Given the above information, which input is the variable input? Explain why this is your answer.

c. Given the above information, what is the price per unit of capital and what is the price per unit of labor?

d. Does this firm experience diminishing returns to labor? To answer this question you will find it helpful to calculate the values for the marginal product of labor, MP_l. Here's a table to use in calculating these values. Make sure you provide the units of measurement in your answers. If necessary, round your answers to the nearest hundredth.

5. Suppose a monopolist can be described by the following equations:

Monopolist's demand curve: P = 250 - 5Q

MC for the monopolist: MC = 30

Assume that the monopolist has no fixed costs

a. Determine the profit maximizing level of output for this monopolist if it charges a single price. Determine the profit maximizing quantity and the level of the monopolist's profit. Show your work. Also, enter your answers in the table below (you will be adding to this table throughout your work on this problem).

b. Suppose this monopolist decides that it will charge 2 prices: $140 for the first 22 units and $100 for the next 8 units. Determine the profit the monopolist will earn when it charges two prices and then enter your answers into the above table. Show how you found your answers.

c. Suppose this monopolist decides to be a perfect price discriminator. What quantity of the good will the monopolist choose to produce? Explain your answer. Then, calculate the value of the monopolist's profit if the monopolist is a perfect price discriminator. Show your work and then enter your answers in the above table.

d. From your analysis in (a) through (c), what conclusion do you draw about price discrimination? Explain your answer fully.

6. Consider a monopolist who sells her product to two different classes of customers. Suppose this monopolist knows the following information:

Demand for product from class one: P = 10 - Q

Demand for product from class two: P = 5 - (1/2)Q

MC = $2 per unit; and assume there are no fixed costs for this monopolist

a. Find the market demand curve for the monopolist's product if there are only these two classes of buyers. Make sure you identify any ranges (or domains) where appropriate.

b. If the monopolist charges a single price to all the buyers of its product, what price will she charge and how many units will the monopolist produce? Show how you found this price and quantity. Then, calculate the amount of profits the monopolist will earn with this combination of price and quantity.

c. Suppose this monopolist decides to engage in third degree price discrimination. What price and quantity will she provide to class one buyers? What price and quantity will she provide to class two buyers? What will profits from class one be for this price discriminating monopolist? What will profits from class two be for this price discriminating monopolist? What will total profits be for this price discriminating monopolist? Is it profitable to engage in third degree price discrimination? Explain your answers fully.