Final answer:
The profit-maximizing quantity in the short-run for a firm in perfect competition is determined by equating the market wage to the marginal revenue product. Firms might increase production due to a market price increase, technological advancements, reduction in wage rates, or anticipation of future market growth.
Step-by-step explanation:
To solve for the profit-maximizing quantity of a representative firm in the short run with the production function Q=ALα, where 0<α<1, and each unit of labor costs w, we equate the marginal cost (MC) with the marginal revenue (MR), which equals the price (P) in perfect competition.
Since labor is the only variable input in the short run, the profit-maximizing condition where the wage (w) equals the marginal revenue product (MRP) must be met. This is represented by the equation P = MR = MC = MRP = w. Firms will increase the quantity of labor until MRP equals w, which will determine their output level.
There are several reasons a representative firm might increase production (Q). First, an increase in market price due to heightened demand encourages firms to expand output to maximize profits. Second, if technological advancements reduce input costs or increase productivity for the firm, it becomes cost-efficient to increase production. Third, a reduction in market wage rates would lower marginal costs, enabling firms to profitably expand output. Finally, firms might increase production in anticipation of future price increases or market expansion.