The accompanying table shows the demand schedule for vitamin...

The accompanying table shows the demand schedule for vitamin D. Suppose that the marginal cost of producing vitamin $\mathrm{D}$ is zero. $$ \begin{array}{c|c} \begin{array}{c} \text { Price of vitamin D } \\ \text { (per ton) } \end{array} & \begin{array}{c} \text { Quantity of vitamin D demanded } \\ \text { (tons) } \end{array} \\ \hline \$ 8 & 0 \\ 7 & 10 \\ 6 & 20 \\ 5 & 30 \\ 4 & 40 \\ 3 & 50 \\ 2 & 60 \\ 1 & 70 \\ \hline \end{array} $$ a. Assume that BASF is the only producer of vitamin $\mathrm{D}$ and acts as a monopolist. It currently produces 40 tons of vitamin $\mathrm{D}$ at $\$ 4$ per ton. If BASF were to produce 10 more tons, what would be the price effect for BASF? What would be the quantity effect? Would BASF have an incentive to produce those 10 additional tons? b. Now assume that Roche enters the market by also producing vitamin $\mathrm{D}$ and the market is now a duopoly. BASF and Roche agree to produce 40 tons of vitamin $\mathrm{D}$ in total, 20 tons each. BASF cannot be punished for deviating from the agreement with Roche. If BASF, on its own, were to deviate from that agreement and produce 10 more tons, what would be the price effect for BASF? What would be the quantity effect for BASF? Would BASF have an incentive to produce those 10 additional tons?

The accompanying table shows the demand schedule for vitamin D. Suppose that the marginal cost of producing vitamin $\mathrm{D}$ is zero.
$$
\begin{array}{c|c}
\begin{array}{c}
\text { Price of vitamin D } \\
\text { (per ton) }
\end{array} & \begin{array}{c}
\text { Quantity of vitamin D demanded } \\
\text { (tons) }
\end{array} \\
\hline \$ 8 & 0 \\
7 & 10 \\
6 & 20 \\
5 & 30 \\
4 & 40 \\
3 & 50 \\
2 & 60 \\
1 & 70 \\
\hline
\end{array}
$$
a. Assume that BASF is the only producer of vitamin $\mathrm{D}$ and acts as a monopolist. It currently produces 40 tons of vitamin $\mathrm{D}$ at $\$ 4$ per ton. If BASF were to produce 10 more tons, what would be the price effect for BASF? What would be the quantity effect? Would BASF have an incentive to produce those 10 additional tons?
b. Now assume that Roche enters the market by also producing vitamin $\mathrm{D}$ and the market is now a duopoly. BASF and Roche agree to produce 40 tons of vitamin $\mathrm{D}$ in total, 20 tons each. BASF cannot be punished for deviating from the agreement with Roche. If BASF, on its own, were to deviate from that agreement and produce 10 more tons, what would be the price effect for BASF? What would be the quantity effect for BASF? Would BASF have an incentive to produce those 10 additional tons?

Key Concepts

Price Effect

The price effect refers to the change in the market price of a good resulting from a change in the total quantity supplied, which typically occurs because the good is sold on a downward?sloping demand curve. When a firm increases its output, the increased aggregate quantity demanded by consumers causes the market price to drop, affecting revenue on all units sold.

Quantity Effect

The quantity effect captures the increase in the total number of units sold as output is raised. Although selling more units can boost revenue, this additional sales gain must be weighed against the loss from lowering the price on all previously sold units, which is a key consideration in marginal revenue calculations.

Marginal Revenue

Marginal revenue is the additional revenue a firm earns by selling one more unit of output, taking into account both the additional sales and the decrease in price that is necessary to sell that extra unit. It is a crucial concept for profit maximization in firms with market power because it helps determine the optimal level of production when marginal revenue equals marginal cost.

Market Demand

Market demand represents the total quantity of a good that consumers are willing and able to purchase at various price levels. The demand schedule, which shows the relationship between the price of the good and the quantity demanded, is essential for understanding how changes in output levels by firms affect the market price and revenue.

Market Structures: Monopoly and Duopoly

The structure of the market significantly influences a firm’s pricing and output decisions. In a monopoly, a single firm controls the market and can manipulate output to maximize profits, whereas in a duopoly the presence of two firms adds strategic interaction, and the decision of one firm can impact the market outcome for both parties. These differences create varying incentives for adherence to or deviation from cooperative agreements.

Collusion and Deviation Incentives

When firms in an oligopolistic market form a collusive agreement, they jointly restrict output to keep prices high and maximize joint profits. However, the temptation to deviate arises because an individual firm may capture additional profit by increasing its own output, even though such a move could harm the collusive equilibrium in the long run. This tension between collective profit maximization and individual incentive to cheat is a central issue in game theory and industrial organization.

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