Question

Draw a diagram for a perfectly competitive firm in long-run equilibrium. Include only the demand curve facing the firm and its \(L R A T C\) curve. Then show the impact of an excise tax (some number of dollars per unit imposed by the government on this firm only but not on any other firm in the market. Can we say what this firm will do in the long run?

Short answer

In the long run, an excise tax imposed only on one firm will increase the firm's costs and move it out of equilibrium. This may lead to an economic loss for the firm. Without additional information, we can't predict with certainty how the firm will react. It may attempt to lower other costs, try to increase their price, or potentially exit the market if the loss is sustained.

Step-by-step solution

Draw the Initial Diagram

Start by drawing a diagram for a perfectly competitive firm in long-run equilibrium. The x-axis should represent the Quantity (Q), while the y-axis represents the Price (P) and Cost (C). Draw the LRATC curve which is U-shaped, representing the firm's long-run average total cost. Then, draw a horizontal line representing the demand curve (named as P=MR) at the minimum point of the LRATC curve, indicating the firm is operating where P=MR=LRATC, which is the condition for long run equilibrium in perfect competition.

Include the Excise Tax

Next, show the effect of the excise tax. The tax increases the firm's costs. To sketch this on your diagram, draw a new LRATC curve above the original LRATC curve with the vertical distance between the two curves equal to the tax per unit. The new curve reflects the additional cost due the excise tax.

Analyze the Impact on the Firm

With the new cost curve, the price the firm can sell at (still indicated by the demand curve) is less than its costs, creating an economic loss. We can't say exactly what the firm will do in the long run without further information, but some possibilities include finding ways to reduce other costs, attempting to increase their price (likely not possible in perfect competition), or exiting the market.

Key concepts

Excise Tax Impact on Firms

When a government imposes an excise tax on a product, it directly affects firms by increasing the cost of producing that product. For a perfectly competitive firm, this tax translates into an upward shift in their long-run average total cost (LRATC) curve.

An excise tax is a per-unit tax, meaning it gets added to each unit of product the firm sells. For example, if the government imposes a \(1 excise tax on every widget produced, the firm's cost to produce each widget increases by \)1. On a graph, this is demonstrated by drawing a new LRATC curve vertically above the original curve, with the distance between them representing the per-unit tax.

In the short-term, firms must contend with the increased costs, which might lead them to raise prices. However, in a perfectly competitive market, the firm is a price taker and cannot easily pass these costs on to consumers. If unable to raise prices due to market competition, the firm's only option is to absorb the cost, leading to reduced profits or potentially incurring losses.

Ultimately, the firm will try to adjust in the long run. It might attempt to increase efficiencies, adopt cost-saving technologies, or it may have no choice but to shut down if it cannot cover the additional costs imposed by the tax.

Long-Run Average Total Cost (LRATC)

The long-run average total cost (LRATC) curve represents all possible production costs for a firm over time, assuming that all inputs can be varied. It's distinctive because it reflects the 'scale' economies, suggesting that up to a point, bigger can indeed be more efficient. The LRATC curve is usually U-shaped, showing economies of scale on the downward slope, constant returns to scale at the bottom flat section, and diseconomies of scale on the upward slope.

The bottom point of the LRATC curve, where it is at its minimum, indicates the most cost-efficient scale of production for a firm. At this point, a firm in a perfectly competitive market will be in long-run equilibrium, selling its goods or services where price equals marginal revenue and marginal cost, leading to neither an economic profit nor loss.

However, shifts in the LRATC curve can dramatically affect a firm's equilibrium. A tax, as previously mentioned, or changes in technology can cause this curve to move. Understanding the LRATC is crucial because it influences the firm's decisions regarding production levels and adjustments needed for maintaining profitability.

Economic Loss in Perfect Competition

The ideal scenario for firms in a perfectly competitive market is to break even in the long run, where the economic profit is zero. This happens because any short-term profits attract new firms to the market, increasing supply until prices drop to the point where profits are eliminated. Conversely, if firms incur losses, some will exit the market, reducing the supply and raising prices until losses are mitigated.

An economic loss occurs when a firm's total revenue is less than its total costs, including opportunity costs of production. This can be due to inefficiencies, high production costs, or price pressures in the market. In the long run, persisting economic losses prompt firms to leave the market, as constant losses are unsustainable.

Diagrammatically, an economic loss is observed when the price at which the firm can sell its product (on the demand curve) is below the LRATC. This gap indicates losses since average costs are not being covered. A firm facing such losses may try to reduce costs or innovate to regain profitability. If these strategies are ineffective, the firm may have no alternative but to cease operation, as their presence in the market is not sustainable.