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Chapter 12: Problem 12

The dominant firm model can help us understand the behavior of some cartels. Let's apply this model to the OPEC oil cartel. We will use isoelastic curves to describe world demand \(W\) and noncartel (competitive supply \(S\). Reasonable numbers for the price elasticities of world demand and noncartel supply are \(-1 / 2\) and \(1 / 2,\) respectively. Then, expressing \(W\) and \(S\) in millions of barrels per day \((\mathrm{mb} / \mathrm{d}),\) we could write \\[ W=160 P^{-1 / 2} \\] and \\[ S=\left(3 \frac{1}{3}\right) P^{1 / 2} \\] Note that OPEC's net demand is \(D=W-S\) a. Draw the world demand curve \(W\), the non-OPEC supply curve \(S,\) OPEC's net demand curve \(D,\) and OPEC's marginal revenue curve. For purposes of approximation, assume OPEC's production cost is zero. Indicate OPEC's optimal price, OPEC's optimal production, and non-OPEC production on the diagram. Now, show on the diagram how the various curves will shift and how OPEC's optimal price will change if non-OPEC supply becomes more expensive because reserves of oil start running out. b. Calculate OPEC's optimal (profit-maximizing) price. (Hint: Because OPEC's cost is zero, just write the expression for OPEC revenue and find the price that maximizes it.) c. Suppose the oil-consuming countries were to unite and form a "buyers' cartel" to gain monopsony power. What can we say, and what can't we say, about the impact this action would have on price?

Short Answer

Expert verified
The OPEC's optimal price would be computed by maximizing the revenue equation. Any shift in the non-OPEC supply would result in an equivalent change in the optimal price. Formation of a 'buyers' cartel' may have an impact on prices, but specific outcomes cannot be determined without additional information.

Step by step solution

01

- Understand the given data

The given data provides us with the world demand \(W\) and noncartel supply \(S\) equations. Also, the student is given the price elasticities of both world demand and noncartel supply.
02

- Draw the curves

Make a diagram with price on the y-axis and quantity on the x-axis. Plot the graphs for the world demand curve \(W\), the non-OPEC supply curve \(S\), OPEC's net demand curve \(D\), and OPEC's marginal revenue curve (which is a horizontal line at price equals zero, as there is no cost to OPEC).
03

- Identify OPEC’s Optimal Price & Production

Locate the point where the net demand curve \(D = W - S\) intersects the marginal revenue curve. The corresponding price on the y-axis is the optimal (profit-maximizing) price for OPEC.
04

- Change in non-OPEC supply

If non-OPEC supply becomes more expensive due to oil reserves running out, the supply curve \(S\) would shift upwards. This would consequently shift the net demand curve \(D\) downwards, leading to an increase in OPEC's optimal price.
05

- Calculate OPEC’s Optimal Price

Given that OPEC's cost is zero, we calculate OPEC's optimal price by maximizing its revenue, given by \(R = P \times D\). Maximizing revenue, we get the equation \(\frac{dR}{dP}=0\). Solving this, we get the OPEC optimal price.
06

- Buyers' Cartel Impact

Finally, if oil-consuming countries were to unite and form a 'buyers' cartel', getting monopsony power, this could potentially influence prices. However, specific impacts cannot be definitively stated without further data on the price elasticity of demand or other relevant data.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

OPEC oil cartel
The Organization of the Petroleum Exporting Countries (OPEC) is an example of a dominant firm model that plays a pivotal role in the global oil market. OPEC acts as a cartel, where member countries work together to control the price and production of oil. By coordinating their efforts, they can influence worldwide oil prices by agreeing on production quotas, which in turn affect the global supply.

Understanding OPEC's behavior provides insight into how large suppliers can affect market dynamics through strategic decisions. Despite their influence, OPEC's decisions are also subject to external factors, like changes in non-OPEC supply, which can affect their ability to maintain desired price levels.
Price elasticity
Price elasticity is a measure of how sensitive the quantity demanded or supplied of a product is to a change in price. In our exercise, numbers for the price elasticities of world demand and noncartel supply are (-1/2) and (1/2), respectively. This means that world demand is inelastic; consumers will not significantly alter their consumption levels with a change in price.

Conversely, noncartel supply is elastic; producers are likely to change their production quantities in response to price shifts. When considering OPEC's decisions, the cartel has to factor in these elasticities to determine their profit-maximizing price. Notably, inelastic demand gives OPEC some leeway to raise prices without losing substantial demand.
Marginal revenue curve
The marginal revenue curve in the context of the dominant firm model plays a critical role in a firm's decision-making process. It represents the additional revenue that a firm earns for each extra unit of goods sold. Ideally, firms seek to produce up to the point where marginal revenue equals marginal cost.

In the case of OPEC, which we can assume has negligible production costs, its marginal revenue curve would be depicted as a line at the price level where revenue is maximized. This curve is crucial for OPEC to determine the most profit-maximizing quantity of oil to produce.
Profit-maximizing price
To find the profit-maximizing price OPEC should set for oil, we need to consider where the cartel's marginal revenue equals marginal costs. However, the task is simplified by the assumption of zero production costs for OPEC. Therefore, we maximize revenue directly, relying on the relationship between the net demand curve (D) and the price.

The profit-maximizing price will be where OPEC can sell the highest quantity of oil at the highest possible price without significantly reducing demand — a balance struck due to the inelastic nature of world oil demand.
Monopsony power
Monopsony power occurs when there is a single, or a dominant buyer in a market, giving that buyer significant control over the price of goods. In our scenario, the formation of a buyers' cartel represents the creation of monopsony power among oil-purchasing countries.

This collective bargaining power could allow the buyers' cartel to negotiate lower prices by reducing the individual countries' dependence on OPEC supply. However, without concrete data on the group's demand elasticity or its ability to substitute other energy sources, the precise impact of monopsony power on prices remains uncertain.

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Most popular questions from this chapter

Suppose all firms in a monopolistically competitive industry were merged into one large firm. Would that new firm produce as many different brands? Would it produce only a single brand? Explain.

Suppose the market for tennis shoes has one dominant firm and five fringe firms. The market demand is \(Q=400-2 P .\) The dominant firm has a constant marginal cost of \(20 .\) The fringe firms each have a marginal cost of \(\mathrm{MC}=20+5 q\) a. Verify that the total supply curve for the five fringe firms is \(Q_{f}=P-20\) b. Find the dominant firm's demand curve. c. Find the profit-maximizing quantity produced and price charged by the dominant firm, and the quantity produced and price charged by each of the fringe firms. d. Suppose there are 10 fringe firms instead of five. How does this change your results? e. Suppose there continue to be five fringe firms but that each manages to reduce its marginal cost to \(\mathrm{MC}=20+2 q\). How does this change your results?

Two firms produce luxury sheepskin auto seat covers: Western Where (WW) and B.B.B. Sheep (BBBS). Each firm has a cost function given by \\[ C(q)=30 q+1.5 q^{2} \\] The market demand for these seat covers is represented by the inverse demand equation \\[ P=300-3 Q \\] where \(Q=q_{1}+q_{2},\) total output. a. If each firm acts to maximize its profits, taking its rival's output as given (i.e., the firms behave as Cournot oligopolists), what will be the equilibrium quantities selected by each firm? What is total output, and what is the market price? What are the profits for each firm? b. It occurs to the managers of WW and BBBS that they could do a lot better by colluding. If the two firms collude, what will be the profit-maximizing choice of output? The industry price? The output and the profit for each firm in this case? c. The managers of these firms realize that explicit agreements to collude are illegal. Each firm must decide on its own whether to produce the Cournot quantity or the cartel quantity. To aid in making the decision, the manager of \(\mathrm{WW}\) constructs a payoff matrix like the one below. Fill in each box with the profit of \(\mathrm{WW}\) and the profit of BBBS. Given this payoff matrix, what output strategy is each firm likely to pursue? d. Suppose WW can set its output level before BBBS does. How much will WW choose to produce in this case? How much will BBBS produce? What is the market price, and what is the profit for each firm? Is WW better off by choosing its output first? Explain why or why not.

Consider two firms facing the demand curve \(P=50-5 Q\), where \(Q=Q_{1}+Q_{2}\). The firms' cost functions are \(C_{1}\left(Q_{1}\right)=20+10 Q_{1}\) and \(C_{2}\left(Q_{2}\right)=10+12 Q_{2}\) a. Suppose both firms have entered the industry. What is the joint profit- maximizing level of output? How much will each firm produce? How would your answer change if the firms have not yet entered the industry? b. What is each firm's equilibrium output and profit if they behave noncooperatively? Use the Cournot model. Draw the firms' reaction curves and show the equilibrium. c. How much should Firm 1 be willing to pay to purchase Firm 2 if collusion is illegal but a takeover is not?

Two firms compete in selling identical widgets. They choose their output levels \(Q_{1}\) and \(Q_{2}\) simultaneously and face the demand curve \\[ P=30-Q \\] where \(Q=Q_{1}+Q_{2}\). Until recently, both firms had zero marginal costs. Recent environmental regulations have increased Firm 2 's marginal cost to \(\$ 15 .\) Firm 1 's marginal cost remains constant at zero. True or false: As a result, the market price will rise to the monopoly level.
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