Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 19: Problem 7

Suppose demand for crude oil is given by \\[ Q=-2,000 P+70,000 \\] where \(Q\) is the quantity of oil in thousands of barrels per year and \(P\) is the dollar price per barrel. Suppose also that there are 1,000 identical small producers of crude oil, each with marginal costs given by \\[ M C=q+5 \\] where \(q\) is the output of the typical firm. a. Assuming each small oil producer acts as a price taker, calculate the market supply curve and the market equilibrium price and quantity. b. Suppose a practically infinite supply of crude oil is discovered in New Jersey by a wouldbe price leader and can be produced at a constant average and marginal cost of \(\$ 15\) per barrel. Assuming the supply behavior of the competitive fringe described in part (a) is not changed by this discovery, how much should the price leader produce in order to maximize profits? What price and quantity will now prevail in the market? c. Graph your results. Does consumer surplus increase as a result of the New Jersey oil discovery? How does consumer surplus after the discovery compare to what would exist if the New Jersey oil were supplied competitively?

Short Answer

Expert verified
Question: Using the given demand and marginal cost functions, find the market supply curve, market equilibrium price and quantity, analyze the impact of a price leader with a constant marginal cost, and compare consumer surpluses. Demand function: Q = -2000P + 70000 Marginal cost function for each small producer: MC = q + 5 Solution (a): Individual firm supply curve and market equilibrium Step 1: Calculate the individual firm's supply curve from the marginal cost. P = MC P = q + 5 Step 2: Calculate the market supply curve by aggregating individual firm's supply curves. There are 1,000 identical small producers. So,  Qs = 1000q Step 3: Equate market demand and market supply to find the equilibrium price and quantity. Q = -2000P + 70000 Qs = 1000q Equating Q and Qs, and solving for P and q.

Step by step solution

01

Calculate the individual firm's supply curve from the marginal cost.

In order to determine the market supply curve, we first need to find the individual firm's supply curve from the marginal cost function \(MC=q+5\). Since firms are price takers, they will set their output level where price equals marginal cost (\(P=MC\)).
02

Calculate the market supply curve by aggregating individual firm's supply curves.

There are 1,000 identical small producers. So, to find the market supply curve (\(Q_s\)), we need to multiply the individual firm's output level by the number of firms: \(Q_s=1000q\).
03

Equate market demand and market supply to find the equilibrium price and quantity.

To find the market equilibrium, we will equate the demand function \(Q=-2000P+70000\) with the supply function \(Q_s=1000q\). Then, we will solve for the equilibrium price, \(P^*\), and corresponding quantity, \(Q^*\). For part (b):
04

Determine the price setter's monopoly price and quantity.

With an infinite supply of crude oil at a constant average and marginal cost of \(15 per barrel, the price leader will act as a monopolist. Determine the price and corresponding quantity where the price leader's marginal cost (\)MC = 15\() is equal to the market demand's marginal revenue (\)MR$).
05

Calculate the market price and quantity.

Now that the price leader's monopoly price and quantity are determined, find the market price and quantity, considering the competitive fringe's supply behavior remains unchanged. For part (c):
06

Graph the market demand, market supply, and price leader's marginal cost.

Graph the initial market demand curve, the market supply curve, and the price leader's marginal cost curve on a single graph, and mark the initial equilibrium point.
07

Graph the new market price and quantity with the price leader.

On the same graph, identify the new equilibrium point, which indicates the new market price and quantity after the price leader enters the market with an infinite supply of crude oil at a constant marginal cost of $15 per barrel.
08

Analyze consumer surplus before and after the oil discovery.

Determine whether consumer surplus has increased or decreased as a result of the increased oil supply from New Jersey and compare it to the consumer surplus if the New Jersey oil were supplied competitively instead of being monopolized by a single price leader. The step-by-step solutions for each part will help the student in understanding the core principles of market equilibrium, demand curve, supply curve, and consumer surplus with a practical example.

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

Assume for simplicity that a monopolist has no costs of production and faces a demand curve given by \\[ Q=150-P \\] a. Calculate the profit-maximizing price-quantity combination for this monopolist. Also calculate the monopolist's profits. b. Suppose a second firm enters the market. Let \(q_{1}\) be the output of the first firm and \(q_{2}\) the output of the second. Market demand is now given by \\[ q_{1}+q_{2}=150-P \\] Assuming this second firm also has no costs of production, use the Cournot model of duopoly to determine the profit-maximizing level of production for each firm as well as the market price. Also calculate each firm's profits. c. How do the results from parts (a) and (b) compare to the price and quantity that would prevail in a perfectly competitive market? Graph the demand and marginal revenue curves and indicate the three different price-quantity combinations on the demand curve.

Suppose a firm is considering investing in research that would lead to a cost- saving innovation. Assuming the firm can retain this innovation solely for its own use, will the additional profits from the lower (marginal) costs be greater if the firm is a competitive price taker or if the firm is a monopolist? Develop a careful graphical argument. More generally, develop a verbal analysis to suggest whether competitive or monopoly firms are more likely to adopt cost-saving innovations. (For an early analysis of this issue, see W. Fellner, "The Influence of Market Structure on Technological Progress," Quarterly Journal of Economics [November 1951]: \(560-567\).)

Suppose a firm's costs for dollars spent on product differentiation (or advertising) activities \((z)\) and quantity \((q)\) can be written as \\[ T C=g(q)+z \quad g^{\prime}(q)>0 \\] and that its demand function can be written as \\[ q=q(P, z) \\] Show that the firm's profit-maximizing choices for \(P\) and \(z\) will result in spending a share of total revenues on \(z\) given by \\[ \frac{z}{P q}=-\frac{e_{q, z}}{e_{q, P}} \\]

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 this monopolist. Also calculate the monopolist's profits. b. Suppose a second firm enters the market. Let \(q_{1}\) be the output of firm 1 and \(q_{2}\) the output of firm 2. Market demand now is given by \\[ q_{1}+q_{2}=53-P \\] Assuming firm 2 has the same costs as firm \(1,\) calculate the profits of firms 1 and 2 as functions of \(q_{1}\) and \(q_{2}\) c. Suppose (after Cournot) each of these two firms chooses its level of output so as to maximize profits on the assumption that the other's output is fixed. Calculate each firm's "reaction function," which expresses desired output of one firm as a function of the other's output. d. On the assumption in part (c), what is the only level for \(q_{1}\) and \(q_{2}\) with which both firms will be satisfied (what \(q_{1}, q_{2}\) combination satisfies both reaction curves)? e. With \(q_{1}\) and \(q_{2}\) at the equilibrium level specified in part (d), what will be the market price, the profits for each firm, and the total profits earned? f. Suppose now there are \(n\) identical firms in the industry. If each firm adopts the Cournot strategy toward all its rivals, what will be the profit- maximizing output level for each firm? What will be the market price? What will be the total profits earned in the industry? (All these will depend on \(n .\) ) g. Show that when \(n\) approaches infinity, the output levels, market price, and profits approach those that would "prevail" in perfect competition.

One way of measuring the size distribution of firms is through the use of the Herfindahl Index, which is defined as \\[ \boldsymbol{H}=\sum \boldsymbol{\alpha}_{i}^{2} \\] where \(\alpha_{i}\) is the share of firm \(i\) in total industry revenues. Show that if all firms in the industry have constant returns-to-scale production functions and follow Cournot output decisions (Equation 19.10 ), the ratio of total industry profits to total revenue will equal the Herfindahl Index divided by the price elasticity of demand. What does this result imply about the relationship between industry concentration and industry profitability?
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