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Suppose a firm must pay an annual tax, which is a fixed sum, independent of whether it produces any output. a. How does this tax affect the firm's fixed, marginal, and average costs? b. Now suppose the firm is charged a tax that is proportional to the number of items it produces. Again, how does this tax affect the firm's fixed, marginal, and average costs?

Short Answer

Expert verified
Fixed sum tax increases both fixed and average costs, while leaving marginal cost unaffected. A tax proportional to output increases marginal and average costs.

Step by step solution

01

Fixed Sum Tax Impact

As given, a fixed sum tax is independent of the level of output. Therefore, it directly increases the firm's fixed costs. Since marginal costs are the costs of producing one more unit, the fixed sum tax will have no impact on marginal costs as it does not depend on the level of output. Average costs, which are the total costs (fixed plus variable) divided by number of units produced, will also increase. This is because while the numerator in the average cost calculation increases (due to increased fixed costs), the denominator remains the same.
02

Proportional Tax Impact

When taxed proportionally to the number of items produced, the tax directly affects variable costs as the amount paid changes with the level of production. Therefore, the firm's marginal costs increase as the cost for producing an extra unit now includes the variable cost plus the tax for that unit. Finally, average costs also increase, as the additional proportional tax contributes to the overall costs of production and gets factored into the average cost calculation.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Fixed Sum Tax Effect
When a firm is subject to a fixed sum tax, it faces an additional expenditure that does not fluctuate with its level of production. This type of tax policy imposes a constant financial burden on the business, regardless of how much or how little it produces. As a result, the fixed sum tax adds to the firm's total fixed costs, which are expenses that occur even when production is zero.

The immediate implication is that the firm's average cost curves shift upward. With average cost defined as the total cost divided by the quantity produced, the introduction of a fixed sum tax means that, at each level of output, the firm must now spread this additional fixed cost over its products. Consequently, the average cost of each good rises. However, since the fixed sum tax is not influenced by the number of units produced, it does not alter the marginal cost. The marginal cost, the cost of producing one additional unit, remains unaffected because this tax is the same amount regardless of output level.

Hence, while the fixed cost increases the hurdle for the firm to start producing, it does not change the economic dynamics of producing 'one more unit'. This distinction is critical for understanding how different types of taxes impact production decisions and firm behavior.
Marginal Cost
Marginal cost plays a central role in the economics of a firm's production decisions. It represents the change in a firm's total cost when it produces an additional unit of output. In simple terms, for each extra product the company decides to make, the marginal cost tells us how much the total cost will go up.

For a firm with no taxes, or just a fixed sum tax, the marginal cost is solely dependent on the variable costs associated with producing one more unit, such as materials and labor. Marginal cost is crucial in the firm's decision-making, as it helps determine the level of production that maximizes profit. When the price of a good is greater than the marginal cost, the firm can increase profits by producing more of it. Conversely, if the price is less than the marginal cost, the firm would reduce production to maximize profits.

This concept helps explain why changes to a firm's cost structure, such as the introduction of a tax, are essential. They impact not only the firm's profitability but also its overall supply of products to the market. Understanding marginal costs allows students and economists to predict how firms will react to different economic policies and market conditions.
Average Cost
Average cost, also known as unit cost, is computed by dividing the total cost of production by the quantity of output produced. It comprises both fixed and variable costs. Fixed costs, such as rent and salaries, are constant regardless of the level of production, while variable costs fluctuate with the production volume. Average cost is an indicator of efficiency; the lower the average cost, the more efficiently a firm is utilizing its resources.

The average cost curve typically shows a 'U' shape due to economies of scale. Initially, as production increases, the firm can spread out its fixed costs over more units, lowering the average cost. However, after reaching a certain production level, inefficiencies begin to creep in, leading to an increase in the average cost.

Taxes that impact the firm's cost structure, such as a fixed sum tax, will invariably influence the average cost. While the fixed sum tax raises the average cost by increasing the total fixed cost, it doesn't change the shape or nature of the average cost curve. It's a vertical lift, meaning that at every level of production, the firm faces a higher cost per unit than before.
Proportional Tax Effect
A proportional tax changes the calculations substantially compared to a fixed sum tax. This tax type is directly tied to the level of output; as production increases, the tax bill goes up. This directly impacts variable costs because the amount of tax paid grows with each additional unit produced. A proportional tax, by definition, adds a cost per unit of output and, therefore, increases the marginal cost.

Since it raises the cost of production for every additional unit, a proportional tax will result in a steeper slope of the marginal cost curve. This adjustment means that firms will reach the profit-maximizing level of production at a lower quantity than they would without the tax. It also impacts average costs, as the heightened marginal cost at each unit of output raises the average cost across all levels of production. Essentially, a proportional tax makes it more expensive to produce, which can lead to reduced output and higher prices for consumers, assuming the market conditions allow for price adjustments.

In essence, the marginal cost and average cost are dynamic figures that respond to changes in fiscal policies such as taxes. A firm's cost structure, influenced by these types of taxes, is a determining factor in production decisions and general economic outcomes.

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Most popular questions from this chapter

A recent issue of Business Week reported the following: During the recent auto sales slump, GM, Ford, and Chrysler decided it was cheaper to sell cars to rental companies at a loss than to lay off workers. That's because closing and reopening plants is expensive, partly because the auto makers' current union contracts obligate them to pay many workers even if they're not working. When the article discusses selling cars "at a loss," is it referring to accounting profit or economic profit? How will the two differ in this case? Explain briefly.

The cost of flying a passenger plane from point \(A\) to point \(B\) is \(\$ 50,000 .\) The airline flies this route four times per day at 7 AM, 10 AM, 1 PM, and 4 PM. The first and last flights are filled to capacity with 240 people. The second and third flights are only half full. Find the average cost per passenger for each flight. Suppose the airline hires you as a marketing consultant and wants to know which type of customer it should try to attract- the off-peak customer (the middle two flights) or the rush-hour customer (the first and last flights). What advice would you offer?

Suppose that a paving company produces paved parking spaces \((q)\) using a fixed quantity of land \((T)\) and variable quantities of cement (C) and labor (L). The firm is currently paving 1000 parking spaces. The firm's cost of cement is \(\$ 4,000\) per acre covered, and its cost of labor is \(\$ 12 /\) hour. For the quantities of \(C\) and \(L\) that the firm has chosen, \(M P_{C}=50\) and \(M P_{L}=4\) a. Is this firm minimizing its cost of producing parking spaces? How do you know? b. If the firm is not cost-minimizing, how must it alter its choices of \(C\) and \(L\) in order to decrease cost?

A computer company produces hardware and software using the same plant and labor. The total cost of producing computer processing units \(H\) and software programs \(S\) is given by \\[\mathrm{TC}=a H+b S-\mathrm{cHS}\\] where \(a, b,\) and \(c\) are positive. Is this total cost function consistent with the presence of economies or diseconomies of scale? With economies or diseconomies of scope?

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