Question

Kyle, Stan, and Eric have created a new app that enables someone to point a smartphone at a person's face while he or she is talking and tell you the probability that he or she is lying. They originally spent \(\$ 80,000\) to develop and patent the app. They could sell the patent to a large firm for \(\$ 1,000,000\) and get out of the business, but it would take them a year to arrange the sale. Currently, they are selling the app themselves, charging the profit-maximizing price of \(\$ 10\) per download and selling 1,000 downloads per year. The only actual payment they make to run the business is a flat \(\$ 200\) per month \((\$ 2,400 \text { per year })\) to an Internet service provider. The interest rate in the economy - which they could earn on alternative investments-is \(5 \%\) per year. a. What is the annual accounting profit of their business? b. What is the annual economic profit of their business? c. Based on the information given in the problem, what is the marginal cost of selling another download? d. Based on the answers above, should Kyle, Stan, and Eric continue to run the business in the short run (the next few months)? e. Based on the answers above, and assuming economic and accounting profit remain unchanged in the long run, should Kyle, Stan, and Eric continue to run the business in the long run (the next few years)? f. One day Kyle thinks he's discovered that demand for their apps is elastic over the entire price range from \(\$ 15\) to \(\$ 5\) per download. If Kyle is correct, should they keep the price at \(\$ 10 ?\) Lower it? Raise it? Explain your answer briefly.

Short answer

a. The annual accounting profit is \$7,600. b. The annual economic profit is -\$42,400. c. The marginal cost of selling another download is \$0. d. They should continue to run the business in the short run as accounting profit is positive. e. They should not continue to run the business in the long run as the economic profit is negative. f. They should lower the price as the demand is elastic.

Step-by-step solution

Calculate Annual Accounting Profit

Accounting Profit will be total annual revenue minus explicit costs. Total revenue (TR) is \( $10 \times 1,000 = $10,000 \). Explicit costs are the amount paid to the Internet service provider annually \( $200 \times 12 = $2,400 \). Therefore, the accounting profit (AP) is \(TR - Explicit Costs = $10,000 - $2,400 = $7,600\).

Calculate Annual Economic Profit

Economic Profit will be total annual revenue minus explicit costs and implicit costs. The implicit cost is interest rate multiplied with the asset that can be sold. Therefore, implicit cost (IC) is \( 0.05 \times 1,000,000 = $50,000 \). The economic profit (EP) is \(TR - Explicit Costs - IC = $10,000 - $2,400 - $50,000 = -$42,400\).

Calculate Marginal Cost

The marginal cost (MC) is the cost of producing one more unit of a good. Here, the boys do not have to pay any additional costs when they sell another app so the marginal cost is $0.

Analyze Short Run Business Continuation

In the short run, they should be able to run the business because the accounting profit is positive, $7,600 - even though the economic profit is negative.

Long Run Business Continuation

In the long run, the economic profit is negative, -$42,400 which suggests that the resources would be better used elsewhere. Therefore, they should not continue the business in the long run.

Price Adjustment after Discovering Elastic Demand

If Kyle is correct about the app's demand being elastic over the entire price range from $15 to $5, then they should lower the price. When demand is elastic, decreased price leads to an increase in total revenue.

Key concepts

Marginal Cost

Understanding marginal cost is critical in the decision-making process for producers, as it represents the change in total cost when producing one additional unit of a product. In the case of Kyle, Stan, and Eric’s app, the exercise suggests that the marginal cost (\text{MC}) is \(0. This is because there are no additional costs associated with selling one more download of their app; the \)200 monthly payment to their Internet service provider covers all the downloads.

It's important to realize that if the \text{MC} were higher than the price at which the app is sold, the company would incur a loss on every additional sale. Hence, even with a negative economic profit, the lack of marginal cost supports the decision to continue operations in the short term, as each additional app downloaded is pure profit from an accounting perspective.

In a broader context, businesses strive to set their selling price above the \text{MC} to ensure a profit margin. However, it is vital to consider other factors such as fixed costs, competition, and market demand when making pricing and production decisions.

Price Elasticity of Demand

Price elasticity of demand measures how sensitive the quantity demanded of a good is to its price. In layman's term, it shows how drastically buyers will cut back or increase their purchase quantities when the price goes up or down. For Kyle and his friends, understanding the price elasticity of their app’s demand is essential for pricing strategy.

As revealed in the exercise, Kyle believes that their app's demand is elastic between the price range of \(5 to \)15, which means that a price decrease will lead to a more than proportional increase in quantity demanded, potentially raising total revenue. In this scenario, if Kyle's assumption is correct, reducing the price of the app could be a strategic move as it might entice more users to download the app, thus possibly offsetting the price cut through higher sales volume.

An elastic demand often correlates with non-essential goods, availability of substitutes, and a significant portion of a consumer’s budget being spent on the good. Firms with products having elastic demand must be cautious in raising prices, as it could lead to a significant drop in sales volume and revenue.

Implicit and Explicit Costs

Explicit costs are out-of-pocket expenses, measurable cash outflows that businesses incur to keep the operation running, like rent, utility bills, and monthly payments to vendors. For the trio’s app business, the explicit cost is the \(200 paid monthly to the Internet service provider.

On the other hand, implicit costs are the opportunity costs of utilizing resources that the business already owns, which could have been put to alternative use, potentially earning revenue. In this exercise, the implicit costs include the opportunity cost of not selling the patent for \)1,000,000 and the other investments the team could have made with this money, such as earning a 5% interest rate annually.

While implicit costs do not directly affect a company's cash flow, they are crucial for calculating economic profit, which subtracts both explicit and implicit costs from total revenue. Kyle, Stan, and Eric’s negative economic profit of -$42,400, considering implicit costs, indicates that their resources could potentially yield more value elsewhere. Understanding both explicit and implicit costs helps business owners make informed decisions about the allocation of their resources and whether they are achieving the best possible financial outcomes for their investments.