This question, like the one before, also has to do with the relationship between elasticity and revenue. In this case we know that elasticity is 0.5, meaning demand is inelastic, or %Q < %P

   In particular, %Q = -0.5 x %P. This means that the change in price will be greater in percentage terms (in fact twice as large) than the change in quantity. If the firm increases price, quantity demanded will fall by a smaller percentage amount, increasing revenue.

   The question asks what a monopolist can do to increase profit, not revenue (in this case it's the same thing). If the firm increases price, thus lowering output, its revenues rise. However, since output falls it has to produce less, causing costs to fall. Rising revenue + falling costs mean increased profit. Since the firm is a monopolist it need not be concerned with competitors; therefore, raising the price increases profits if demand is inelastic.

6. A monopolist learns that the own price elasticity of a product it manufactures is 0.5. What would be the correct action for this firm to take if it wishes to increase its profits?

1. Raise the price because demand for the product is inelastic. As explained above, the correct answer.
2. Lower the price because demand for the good is elastic. Wrong, because demand is both inelastic and price should be increased. If demand were elastic, lowering the price would increase revenues but we couldn't be sure about profit in this case without cost information.
3. We need information on the firm's cost structure in order to answer this question. As we noted above, we don't need any cost info since lowering output is guaranteed to reduce costs.
4. Raise the price because demand is elastic. Wrong because demand is inelastic. If demand were elastic raising the price would lower profits.
5. Lower the price because demand is inelastic. It is true that demand is inelastic. However, lowering the price would reduce revenue and increase sales, thereby raising costs and causing profits to fall.