Question

Suppose that Tommy Hilfiger's marginal cost of a jacket is a constant \(\$ 100\) and the total fixed cost at one of its stores is \(\$ 2,000\) a day. This store sells 20 jackets a day, which is its profit-maximizing number of jackets. Then the stores nearby start to advertise their jackets. The 'lommy Hilfiger store now spends \(\$ 2,000\) a day advertising its jackets, and its profit-maximizing number of jackets sold jumps to 50 a day. a. What is this store's average total cost of a jacket sold (i) before the advertising begins and (ii) after the advertising begins? b. Can you say what happens to the price of a Tommy Hilfiger jacket, Tommy's markup, and Tommy's economic profit? Why or why not?

Short answer

Average total cost before advertising: \(200. Average total cost after advertising: \)180. Specific impacts on price, markup, and economic profit are indeterminate without further details.

Step-by-step solution

Title - Define Fixed and Variable Costs Without Advertising

First, identify the fixed and variable costs before advertising. Total fixed cost is provided as \(2000. The marginal cost, which represents the variable cost per jacket, is \)100. Note that marginal cost remains constant regardless of the number of jackets sold.

Title - Calculate Total Cost Without Advertising

Calculate the total cost for selling 20 jackets without advertising. Use the formula for total cost: \[ \text{Total Cost} = \text{Fixed Cost} + (\text{Marginal Cost} \times \text{Quantity}) \]Plug in the values: \[ \text{Total Cost} = 2000 + (100 \times 20) \]\[ \text{Total Cost} = 2000 + 2000 = 4000 \]

Title - Calculate Average Total Cost Without Advertising

Determine the average total cost by dividing the total cost by the quantity sold.\[ \text{Average Total Cost (before)} = \frac{\text{Total Cost}}{\text{Quantity}} \]\[ \text{Average Total Cost (before)} = \frac{4000}{20} = 200 \]

Title - Include Advertising Cost in Fixed Costs

Now, add the daily advertising cost to the total fixed costs. The new fixed cost becomes: \[ \text{Fixed Cost (new)} = 2000 + 2000 = 4000 \]

Title - Calculate Total Cost With Advertising

Calculate the total cost for selling 50 jackets with advertising. Use the same formula for total cost: \[ \text{Total Cost (new)} = \text{Fixed Cost (new)} + (\text{Marginal Cost} \times \text{Quantity}) \]Plug in the values: \[ \text{Total Cost (new)} = 4000 + (100 \times 50) \]\[ \text{Total Cost (new)} = 4000 + 5000 = 9000 \]

Title - Calculate Average Total Cost With Advertising

Determine the average total cost by dividing the total cost by the quantity sold:\[ \text{Average Total Cost (after)} = \frac{\text{Total Cost (new)}}{\text{Quantity}} \]\[ \text{Average Total Cost (after)} = \frac{9000}{50} = 180 \]

Title - Analyze Economic Profit

To understand the impact on economic profit, focus on whether the increased advertising cost resulted in sufficient additional sales revenue to cover the new costs. Without specific information on sales revenue or price change, we cannot definitively ascertain changes in price, markup, or economic profit.

Key concepts

Fixed Costs

Fixed costs are expenses that do not change based on the level of production or sales. In Tommy Hilfiger's case, the fixed cost at the store, before considering advertising, is \(\backslash\backslashtext\{\$ 2000\}\). This amount remains constant regardless of how many jackets the store sells.
Examples of fixed costs can include rentals, salaries of permanent staff, insurance, and maintenance. In this exercise, once advertising begins, a new fixed cost component of \(\backslash\backslashtext\{\$ 2000\}\) is added, making the total fixed costs \(\backslash\backslashtext\{\$ 4000\}\). This demonstrates how fixed costs can sometimes change when new expenses are introduced, but within that new level, they remain constant regardless of sales volume.

Marginal Costs

Marginal cost is the additional cost incurred for producing one more unit of a product. For Tommy Hilfiger, the marginal cost per jacket is a constant \(\backslash\backslashtext\{\$ 100\}\). This means that for each additional jacket produced, the store incurs an additional cost of \(\backslash\backslashtext\{\$ 100\}\).
The marginal cost is important for understanding how total costs grow with increasing production. Even though Tommy’s fixed costs might change due to advertising, the marginal cost per unit remains the same.

Variable Costs

Variable costs change with the level of output. In this case, the variable cost per jacket is equal to the marginal cost, i.e., \(\backslash\backslashtext\{\$ 100\}\) per jacket. The more jackets Tommy Hilfiger produces, the more the total variable costs increase.
If the store sells 20 jackets, the total variable cost is \(\backslash\backslashtext\{20 ∗ 100 = \$ 2000\}\). When the store increases sales to 50 jackets due to advertising, the variable cost rises to \(\backslash\backslashtext\{50 ∗ 100 = \$ 5000\}\).

Economic Profit

Economic profit is different from accounting profit. It includes both explicit costs (like fixed and variable costs) and implicit costs (like opportunity costs). To determine whether the additional advertising expense is beneficial, we need to compare the revenue generated by selling more jackets against the costs incurred.
While the exercise does not provide the revenue numbers, we can infer that for Tommy Hilfiger to maintain or increase economic profit, the increase in revenue from sales due to advertising must outweigh the increased costs.

Advertising Impact

Advertising can significantly impact a business by increasing customer awareness and sales. In Tommy Hilfiger's scenario, advertising doubled the fixed costs but increased the number of jackets sold from 20 to 50 per day.
The average total cost decreased from \(\backslash\backslashtext\{\$ 200\}\) to \(\backslash\backslashtext\{\$ 180\}\) per jacket due to the spread of fixed costs over more units. This indicates that if the advertising effectively boosts sales volume without a proportional increase in variable costs, it can lower the average cost per unit. However, the overall profitability still depends on whether the total revenue covers these increased costs.