Question

A sales tax of $\mathrm{\$}1$ per unit of output is placed on a particular firm whose product sells for $\mathrm{\$}5$ in a competitive industry with many firms. a. How will this tax affect the cost curves for the firm? b. What will happen to the firm's price, output, and profit? c. Will there be entry or exit in the industry?

Short answer

The tax will increase the firm's marginal and average variable costs, leading to a decrease in output, and hence decrease in profit. The firm's price will continue to be determined by market forces. Whether there will be entry or exit in the industry depends on whether the tax affects this specific firm or the entire industry. In the first case, the taxed firm might exit. In the latter case, entries or exits will depend on the impact of the tax on the overall industry profitability.

Step-by-step solution

- Understand the impact on cost curves

The tax of $\mathrm{\$}1$ per unit of output effectively increases the cost of production for every unit the firm produces. This shifts the firm’s marginal cost and average variable cost upward by the amount of the tax, but doesn't affect fixed costs because they do not vary with output. This means the firm now needs higher revenue per unit sold to cover the same level of production.

- Analyze the impact on firm's price, output and profit

In a competitive industry, the firm cannot simply increase the price of the product to offset the tax, due to the competitive pressure from other firms. It's price will still be determined by the market. As its costs increase, the firm will reduce output until the price is again equal to the marginal cost. This will typically lead to lower profit, assuming the tax increases marginal costs more than average cost.

- Determine industry's reaction

If the tax is only imposed on this particular firm, it will be at a disadvantage compared to the other firms in the industry. This could lead to an exit, if the firm cannot cover the marginal costs without sacrificing profitability. If the tax is imposed on the whole industry, then all firms in this industry face the same increase in costs and may experience lower profits, but there won't necessarily be entries or exits unless the new cost structure affects overall industry profitability.

Key concepts

Impact of Sales Tax on Cost Curves

When a sales tax is implemented, such as the $\mathrm{\$}1$ per unit of output in the given exercise, a firm faces immediate adjustments in its cost structure.

This incremental cost acts as an additional variable cost, which directly influences the firm’s cost curves. Specifically, the firm’s marginal cost (MC) and average variable cost (AVC) curves shift upward by the amount of the tax. This is because each additional or marginal unit produced now carries an extra cost due to the tax. The tax does not, however, alter the average fixed cost (AFC) or the fixed cost (FC) since these costs do not change with the level of output.

It's essential to understand that the MC curve dictates the quantity supplied by the firm at any given price while the AVC helps determine if the firm can cover its variable costs at a certain level of production. An upward shift in these curves typically means that less will be supplied at each price level unless there is a corresponding increase in the selling price, which is not a viable strategy in a highly competitive market. Therefore, the tax will likely lead to reduced output and possibly reduced profitability.

Price Dynamics in a Competitive Industry

In a perfectly competitive industry, individual firms are price takers, meaning they have no power to influence the price at which their product sells; they must accept the market price.

Following the imposition of a $\mathrm{\$}1$ sales tax per unit, the firm cannot raise its selling price from $\mathrm{\$}5$ to offset this tax because its competitors, assuming they are not taxed, will continue to provide the product at the lower price. Resultantly, the firm's price remains at the equilibrium set by market demand and supply. With increased costs and a fixed selling price, the firm will reduce its output to the point where the marginal cost, now including the tax, equals the prevailing market price. This balance is crucial for the firm to maximize its profit; otherwise, it would incur losses on additional units produced.

Unfortunately, such cost increases lead to lower profits since the firm's cost per unit sold has increased, constricting the margin between cost and revenue per unit. The crucial takeaway here is that in a competitive market, firms have very minimal wiggle room to deal with cost increases—they must absorb them, reduce output, or eventually cease operations if the cost can't be mitigated.

Industry Entry and Exit Decisions Post-Tax

Industry entry and exit are significantly influenced by profitability. When a sales tax is introduced, it can tip the balance of profitable operation, prompting firms to reassess their position in the market.

If the sales tax is specific to one firm, as in our exercise, this firm is placed at an immediate disadvantage compared to its untaxed rivals. It may experience a profit squeeze that, if severe enough, might lead to its exit from the industry as it becomes no longer viable to continue operations.

Contrastingly, if the tax applies industry-wide, all firms would suffer a profit hit, potentially altering the industry's attractiveness to new entrants. The higher costs might discourage entry because the anticipated returns would be lower, thus leading to a potential reduction in the industry's growth rate. However, existing firms may not exit en masse unless the tax is so oppressive that firms cannot cover their production costs and earn at least their opportunity costs. In equilibrium, the industry might settle at a lower level of total output and higher prices if demand remains unchanged, adjusting to the new cost reality imprinted by the tax.