Question

Bianca bakes delicious cookies. Her total fixed cost is \(\$ 40\) a day, and her average variable cost is \(\$ 1\) a bag. Few people know about Bianca's Cookies, and she is maximizing her profit by selling 10 bags a day for \(\$ 5\) a bag. Bianca thinks that if she spends \(\$ 50\) a day on advertising, she can increase her market share and sell 25 bags a day for \(\$ 5\) a bag. If Bianca advertises, will her average total cost increase or decrease at the quantity produced?

Short answer

The average total cost decreases from \(5\) to \(4.6\) dollars per bag with advertising.

Step-by-step solution

Calculate Total Variable Cost Without Advertising

Total variable cost is calculated by multiplying the number of bags by the average variable cost per bag. Without advertising, Bianca sells 10 bags a day, so the total variable cost is given by: \(TVC = 10 \times 1 = 10\) dollars.

Calculate Total Cost Without Advertising

Total cost is the sum of fixed cost and total variable cost. Without advertising, the fixed cost is \(40\) dollars and the total variable cost is \(10\) dollars. Therefore, total cost is \(TC = 40 + 10 = 50\) dollars.

Calculate Average Total Cost Without Advertising

Average total cost is calculated by dividing the total cost by the quantity produced. Without advertising, the average total cost will be \(ATC = \frac{TC}{Q} = \frac{50}{10} = 5\) dollars.

Calculate Total Variable Cost With Advertising

If Bianca advertises, she will sell 25 bags a day. The total variable cost will then be: \(TVC = 25 \times 1 = 25\) dollars.

Calculate Total Cost With Advertising

The total cost with advertising includes the fixed cost, total variable cost, and advertisement cost. The fixed cost is \(40\) dollars, the total variable cost is \(25\) dollars, and the advertisement cost is \(50\) dollars. Thus, the total cost is: \(TC = 40 + 25 + 50 = 115\) dollars.

Calculate Average Total Cost With Advertising

Average total cost with advertising is calculated by dividing the total cost by the quantity produced. Therefore, the average total cost is: \(ATC = \frac{TC}{Q} = \frac{115}{25} = 4.6\) dollars.

Comparison and Conclusion

Compare the average total cost without advertising (\(5\) dollars per bag) and the average total cost with advertising (\(4.6\) dollars per bag). Since \(4.6\) dollars is less than \(5\) dollars, the average total cost decreases when Bianca advertises.

Key concepts

Fixed Costs

Fixed costs are expenses that do not change regardless of the number of products produced. For Bianca, her fixed costs are \(\$40\) a day. These costs include things like rent, salaries, and equipment. Fixed costs will remain the same whether Bianca sells 1 bag of cookies or 100 bags. This is important because it means that these costs must be covered regardless of her sales volume. Understanding fixed costs helps Bianca determine her baseline expenses.

Variable Costs

Variable costs change with the level of production. In Bianca's case, her average variable cost is \(\$1\) per bag of cookies. This cost includes ingredients like flour, sugar, and chocolate chips. To calculate the total variable cost, you multiply the number of bags by the average variable cost. How? Let's see:

• Without advertising: 10 bags/day \(\rightarrow TVC = 10 \times 1 = 10\) dollars
• With advertising: 25 bags/day \(\rightarrow TVC = 25 \times 1 = 25\) dollars

As you can see, variable costs rise as more cookies are baked.

Advertising Impact on Costs

Advertising can change Bianca's total costs and average total cost. If she spends \(\$50\) on advertising each day, she believes that she can sell 25 bags of cookies instead of 10. Let's look at how her costs break down with advertising.

• Total variable cost increases from \(\$10\) to \(\$25\)
• She incurs an additional \(\$50\) for advertising
• Total cost goes from \(\$50\) (no ads) to \(\$115\) (with ads)

Now, we calculate the average total cost:

• Without advertising: ATC = \(\frac{50}{10} = 5\) \(\$\) per bag
• With advertising: ATC = \(\frac{115}{25} = 4.6\) \(\$\) per bag

Advertising reduces her average total cost per bag.

Profit Maximization

Profit maximization means producing the quantity of goods where profits are highest. Profit is revenue minus total costs.
For Bianca:

• Without advertising: Revenue = 10 bags \(\times \) \(\$5\) per bag = \(\$50\)
• Total Cost = \(\$50\)
• Profit = 50 - 50 = 0 (break-even)

With advertising:

• Revenue = 25 bags \(\times \) \(\$5\) per bag = \(\$125\)
• Total Cost = \(\$115\)
• Profit = 125 - 115 = 10

Advertising helps Bianca increase her profit from \(\$0\) to \(\$10\), showing that it's beneficial for her business.