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Chapter 24: Problem 14

Suppose that a firm has a monopoly on a good with the following demand schedule. \begin{tabular}{cccc} Price & Quantity & Price & Quantity \\ \hline\(\$ 10\) & 0 & \(\$ 4\) & 6 \\ \(\$ 9\) & 1 & \(\$ 3\) & 7 \\ \(\$ 8\) & 2 & \(\$ 2\) & 8 \\ \(\$ 7\) & 3 & \(\$ 1\) & 9 \\ \(\$ 6\) & 4 & \(\$ 0\) & 10 \\ \(\$ 5\) & 5 & & \\ \hline \end{tabular} a. What price and quantity will the monopolist produce at if the marginal cost is a constant \(\$ 4\) b. Calculate the deadweight loss from having the monopolist produce rather than a perfect competitor.

Short Answer

Expert verified
Answer: The deadweight loss is $4.5.

Step by step solution

01

In order to find the revenue-maximizing quantity, we need to find the total revenue function. To do so, we should first write the demand function, with Q = quantity and P = price: \(Q = 10 - P\) To obtain the total revenue function, we multiply the price by the quantity: \(TR(Q) = P * Q = (10 - Q) * Q\) #Step 2: Find the marginal revenue function#

To understand how the revenue changes when the quantity increases, we need to find the marginal revenue function. We obtain the marginal revenue by differentiating the total revenue function with respect to quantity: \(MR(Q) = \frac{dTR(Q)}{dQ} = 10 - 2Q\) #Step 3: Determine the revenue-maximizing quantity given the marginal cost#
02

The monopolist will maximize revenue by producing at the point where marginal revenue (MR) is equal to the marginal cost (MC). In this case, the marginal cost is given as a constant: \( \$ 4\). Setting the MR equal to the MC, we can find the quantity: \(MR(Q) = MC\) \(10 - 2Q = 4\) Now, solve for Q: \(2Q = 6\) \(Q = 3\) #Step 4: Find the monopoly price#

We found that the monopolist's revenue-maximizing quantity is 3 units. Now we will find the corresponding price using the demand function: \(P = 10 - Q\) \(P = 10 - 3\) \(P = \$ 7\) Thus, the monopolist will produce 3 units at a price of \( \$ 7\). #Step 5: Find the competitive equilibrium quantity and price#
03

Under perfect competition, the market will be in equilibrium when the supply function, which is equivalent to the marginal cost, is equal to the demand function: \(P = 10 - Q = MC\) Solving for Q: \(10 - Q = 4\) \(Q = 6\) The competitive equilibrium quantity is 6 units. Now, find the corresponding price: \(P = 10 - Q\) \(P = 10 - 6\) \(P = \$ 4\) Under perfect competition, the market price would be \( \$ 4\). #Step 6: Calculate the deadweight loss#

Finally, we need to calculate the deadweight loss (DWL) resulting from the monopolist's production. DWL = (Competitive quantity - Monopoly quantity) * (Monopoly price - Marginal cost) / 2 DWL = (6 - 3) * (7 - 4) / 2 DWL = 3 * 3 / 2 DWL = 4.5 The deadweight loss due to the monopolist's production compared to perfect competition is \( \$ 4.5\).

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Most popular questions from this chapter

Several electric utilities are providing customers with a choice of billing procedures. Customers can select a time-of-day meter that registers electric usage throughout the day, or they can select a regular meter that registers total usage at the end of the day. With the time-of-day meter, the utility is able to charge customers a much higher rate for peak usage than for nonpeak usage. The regular meter users pay the same rate for electric usage no matter when it is used. Why would the electric utility want customers to choose the time-of-day meter?

Why is it necessary for the seller to be able to keep customers from reselling the product in order for price discrimination to occur? There are many products for which you get a discount for purchasing large quantities. For instance, most liquor stores will provide a discount on wine if you purchase a case. Is this price discrimination? If so, what is to keep one customer from purchasing cases of wine and then reselling single bottles at a price above the case price but below the liquor store’s single-bottle price?

Describe how "quantity discounts" can be price discrimination.

State colleges and universities have two levels of tuition or fees. The less expensive is for residents of the state; the more expensive is for nonresidents. Assume that the universities are profit-maximizing monopolists and explain their pricing policy. Now, explain why the colleges and universities give student aid and scholarships.

In recent years, U.S. car manufacturers have charged lower prices for cars in western states in an effort to offset the competition from Japanese cars. This twotier pricing scheme has upset many car dealers in the eastern states. Many have called it discriminatory and illegal. What conditions are necessary for this pricing scheme to be profitable to the U.S. companies?
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