Two firms decide to form a cartel and collude in a way that maximizes industry profits. Each firm has zero production costs and each firm is given a positive output quota by the cartel. Which of the following statement(s) are NOT true.
(a) Each firm would want to produce more than its quota if it knew that the other would continue to produce at its quota.
(b) The price elasticity of demand will be -1 at the output level chosen.
(c) Output will be lower than if the firms behaved as Cournot firms.
(d) Output will be lower than if the firms behaved as competitors.
I pick (a) and (b) because (a) the problem is a shared monopoly meaning that the duopolists know that they earn more when they form a cartel, and (b) states that the firms will produce in the inelastic portion which is not true since they will have negative marginal revenues and total revenues.
The two firms agree to act as a monopolist. Sinc MC is zero for both firms, they will produce where MC=MR=0 (where MR is the combined MR for both firms). And when MR=0, the elasticity of demand is -1. So b is true.
Now at this optimal production point, each firm producing its quota, if a firm decides to produce one more unit the combined MR would become negative. However the overall decline in MR is shared by both firms, while the increase revenue from the one extra unit goes entirely to the cheating firm; profits of the cheating firm go up. So, a is true.
If the firms suddenly switch to a Cournot model, this is the same as scenario a) -- each firm will treat the other's firm's output as fixed. Each firm will want to increase production. So c) is false.
cournot firms are competitors, and since I contend c) is false, d) must also be false.
Your explanation for selecting options (a) and (b) is mostly correct. Now let's further analyze each statement to verify their accuracy:
(a) Each firm would want to produce more than its quota if it knew that the other would continue to produce at its quota.
This statement is NOT true. In a cartel, firms collude to maximize industry profits. To do so, they agree upon output quotas to ensure higher prices and market control. If one firm were to produce more than its quota while the other firm continued to produce at its quota, it would lead to an increase in industry output and potentially lower prices, resulting in reduced industry profits. Therefore, each firm would not want to produce more than its quota under these circumstances.
(b) The price elasticity of demand will be -1 at the output level chosen.
This statement is NOT true either. The price elasticity of demand measures the responsiveness of quantity demanded to changes in price. In a cartel, firms restrict their output, which can lead to higher prices. However, it does not guarantee a price elasticity of -1. The elasticity of demand depends on various factors, such as the availability of substitutes, consumer preferences, and price levels. Consequently, it is not accurate to assume a price elasticity of -1 at the output level chosen in a cartel.
(c) Output will be lower than if the firms behaved as Cournot firms.
This statement is TRUE. In a Cournot duopoly, firms set their output levels based on their expectations of how the rival firm will react. This results in a higher output compared to a cartel where output is restricted. In a cartel, output is intentionally limited to maximize industry profits, leading to lower output than if the firms behaved as Cournot firms.
(d) Output will be lower than if the firms behaved as competitors.
This statement is TRUE as well. In a perfectly competitive market, firms independently make production decisions based on market forces, resulting in a larger amount of output compared to a cartel. In a cartel, firms coordinate their actions to limit output and increase prices, resulting in lower output than if the firms operated as competitors.
To summarize, the statements that are NOT true are (a) and (b).
Your reasoning is partially correct.
(a) Each firm would actually want to produce exactly its quota if it knew that the other firm would continue to produce at its quota. In a cartel, firms collude to maximize industry profits, which involves strictly following the agreed-upon quotas. If one firm produces more than its quota, it risks increasing output and driving down prices, resulting in lower profits for the industry as a whole.
(b) The price elasticity of demand will not necessarily be -1 at the output level chosen. The price elasticity of demand measures the responsiveness of quantity demanded to changes in price. In this situation, where the firms have zero production costs and collude to maximize profits, they would set the price and output level that maximizes industry profits, regardless of the price elasticity of demand.
(c) and (d) are both true. Output will be lower in a cartel compared to firms behaving as Cournot firms or competitors. In a Cournot duopoly, firms independently choose their output levels, taking into account their rivals' outputs and without colluding. In a competitive market, firms act independently, setting prices and output levels to maximize their own profits.
So, the correct answer is (a) and (b).