A lump sum subsidy will always lead to an increase in a firm's production output because it provides financial support regardless of the quantity produced.

A lump sum subsidy is a fixed amount of money given to a firm, which does not depend on how much the firm produces. This financial support can help cover costs like rent, utilities, or salaries, allowing the firm to operate more smoothly. However, it doesn't directly encourage the firm to produce more goods since the subsidy amount remains the same regardless of output levels. For example, if a bakery receives a lump sum subsidy of $10,000, it can use that money to pay for ingredients or equipment, but it may not necessarily bake more bread if there is no demand for it. Therefore, while a lump sum subsidy provides financial relief, it does not guarantee an increase in production output.