Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 18: Problem 6

Suppose a monopoly produces its output in several different plants and that these plants have differing cost structures, How should the firm decide how much total output to produce? How should it distribute this output among its plants to maximize profits?

Short Answer

Expert verified
Answer: A monopolist should find the profit-maximizing output level by determining its total cost and revenue functions, and then maximize the profit function. Once the profit-maximizing output level is found, the firm should distribute the output among the plants in a way that equalizes their marginal costs, ensuring that the total cost is minimized.

Step by step solution

01

Determine the cost function of each plant

Let's assume we have n plants, with each plant represented by the index i. For each plant i, we need to identify its cost function, which we will represent as C_i(q_i), where q_i is the output of plant i.
02

Find the firm's total cost function

Now that we have determined the cost function for each plant, we need to find the firm's total cost function. It can be found by summing the cost functions of all the plants. The firm's total cost function is given by: C_T(Q) = sum_i C_i(q_i)
03

Determine the demand function faced by the firm

To determine the demand function faced by the firm, we need to know the price that consumers are willing to pay for the firm's output. Let's represent this demand function as P(Q), where Q is the firm's total output.
04

Calculate the firm's total revenue function

Having defined the demand function, we can now calculate the firm's total revenue function. The total revenue function is the product of the demand function (the price at which the firm sells its output) and the total output: TR(Q) = P(Q) * Q
05

Determine the profit-maximizing output level

To find the profit-maximizing output level, we need to determine the profit function and then maximize it. The profit function is given by the difference between the total revenue function and the total cost function: Π(Q) = TR(Q) - C_T(Q) To find the profit-maximizing output level, we need to find the Q that maximizes Π(Q). This can be achieved by taking the derivative of Π(Q) concerning Q, and setting it to zero: dΠ(Q) / dQ = 0 Now, solve for Q to find the profit-maximizing output level.
06

Distribute the output among the plants to minimize costs

Having found the profit-maximizing output level, the final step is to distribute this output among the plants in such a way that the total cost is minimized. To do this, the firm should equate the marginal cost of each plant. The marginal cost of each plant i is the derivative of its cost function concerning q_i: MC_i = dC_i(q_i) / dq_i We can now set the marginal cost of each plant equal to each other until the desired output level is reached: MC_1 = MC_2 = ... = MC_n By equating the marginal costs and using the profit-maximizing output level, the optimal distribution of output among the plants can be determined.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Suppose the market for Hula Hoops is monopolized by a single firm. a. Draw the initial equilibrium for such a market. b. Now suppose the demand for Hula Hoops shifts outward slightly. Show that, in general (contrary to the competitive case), it will not be possible to predict the effect of this shift in demand on the market price of Hula Hoops. c. Consider three possible ways in which the price elasticity of demand might change as the demand curve shifts - it might increase, it might decrease, or it might stay the same. Consider also that marginal costs for the monopolist might be rising, falling, or constant in the range where \(M R=M C\). Consequently, there are nine different combinations of types of demand shifts and marginal cost slope configurations. Analyze each of these to determine for which it is possible to make a definite prediction about the effect of the shift in demand on the price of Hula Hoops.

Suppose a monopoly can produce any level of output it wishes at a constant marginal (and average) cost of \(\$ 5\) per unit. Assume the monopoly sells its goods in two different markets separated by some distance. The demand curve in the first market is given by $$a,=55-p_{n}$$ and the demand curve in the second market is given by $$\mathrm{Q}_{2}=70-2 \mathrm{P}_{2}$$ a If the monopolist can maintain the separation between the two markets, what level of output should be produced in each market, and what price will prevail in each market? What are total profits in this situation? b. How would your answer change if it only cost demanders \(\$ 5\) to transport goods between the two markets? What would be the monopolist's new profit level in this situation? c. How would your answer change if transportation costs were zero and the firm was forced to follow a single-price policy? d. Suppose the firm could adopt a linear two-part tariff under which marginal prices must be equal in the two markets but lump-sum entry fees might vary. What pricing policy should the firm follow?

Suppose a perfectly competitive industry can produce widgets at a constant marginal cost of S10 per unit. Monopolized marginal costs rise to \(\$ 12\) per unit because \(\$ 2\) per unit must be paid to lobbyists to retain the widget producers' favored position, Suppose the market demand for widgets is given by $$d_{D}-1,000-50 P$$ a. Calculate the perfectly competitive and monopoly outputs and prices. b. Calculate the total loss of consumer surplus from monopolization of widget production. c. Graph your results and explain how they differ from the usual analysis.

A monopolist faces a market demand curve given by $$d=70-P$$ a. If the monopolist can produce at constant average and marginal costs of \(\mathrm{AC}=M C=6\) what output level will the monopolist choose in order to maximize profits? What is the price at this output level? What are the monopolist's profits? b. Assume instead that the monopolist has a cost structure where total costs are described by $$T C=.25\left(?^{2}-5 g+300\right.$$ With the monopolist facing the same market demand and marginal revenue, what pricequantity combination will be chosen now to maximize profits? What will profits be? c. Assume now that a third cost structure explains the monopolist's position, with total costs given by $$T C=.0133 Q^{3}-5 Q+250$$ Again, calculate the monopolist's price-quantity combination that maximizes profits. What will profit be? (Hint: Set \(M C=\)MRas usual and use the quadratic formula to solve the second-order equation for \(Q\) d. Graph the market demand curve, the \(M R\) curve, and the three marginal cost curves from parts (a), (b), and (c). Notice that the monopolist's profit- making ability is constrained by (1) the market demand curve (along with its associated Mi? curve) and (2) the cost structure underlying production.

A monopolist can produce at constant average and marginal costs of \(A C=M C=5 .\) The firm faces a market demand curve given by \(Q=53-P\) a. Calculate the profit-maximizing price-quantity combination for the monopolist. Also cal culate the monopolist's profits. b. What output level would be produced by this industry under perfect competition (where price \(=\text { marginal cost }) ?\) c. Calculate the consumer surplus obtained by consumers in case (b). Show that this exceeds the sum of the monopolist's profits and the consumer surplus received in case (a). What is the value of the "deadweight loss" from monopolization?
See all solutions

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free