A.2 For a monopolist having a capacity level k:i. It is always optimal to fix a price for which the quantity sold is equal to k.ii. It is never optimal to fix a price for which quantity sold is equal to k.X The optimal price may imply a quantity sold equal to k.iv. The optimal quantity always implies marginal revenue equal to marginal cost.
Question
A.2 For a monopolist having a capacity level k:i. It is always optimal to fix a price for which the quantity sold is equal to k.ii. It is never optimal to fix a price for which quantity sold is equal to k.X The optimal price may imply a quantity sold equal to k.iv. The optimal quantity always implies marginal revenue equal to marginal cost.
Solution
The statement "The optimal price may imply a quantity sold equal to k" is correct. A monopolist will set a price where marginal cost equals marginal revenue, which may or may not result in the quantity sold being equal to the capacity level k.
The statement "It is always optimal to fix a price for which the quantity sold is equal to k" is not necessarily true. While a monopolist would want to sell all of its capacity, it would not do so if the price it had to charge to sell all of its capacity was below the price where marginal cost equals marginal revenue.
The statement "It is never optimal to fix a price for which quantity sold is equal to k" is also not necessarily true. If the price where marginal cost equals marginal revenue results in a quantity sold that is equal to the capacity level k, then it would be optimal to fix a price for which the quantity sold is equal to k.
The statement "The optimal quantity always implies marginal revenue equal to marginal cost" is generally true. In most cases, a firm will produce up to the point where marginal cost equals marginal revenue to maximize profits. However, there may be exceptions in certain market conditions or for certain types of goods.
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