If a competitive firm's cost increases due to an increase in the price of a factor of production or a tax, the firm's manager can quickly determine by how much to adjust output by calculating how the firm's marginal cost has changed and applying the profit-maximization rule. Suppose that the Canadian province of Manitoba imposes a specific (per-unit) tax of \(t\) per ton of lime produced in the province. No other provincial government imposes such a tax. Manitoba has only one lime-producing firm, so the tax affects only that firm and hence has virtually no effect on the market price. If the tax is imposed, how should the Manitoba firm change its output level to maximize its profit, and how does its maximum profit change?