Jimmy's room overlooks a major league baseball stadium. He...

Jimmy's room overlooks a major league baseball stadium. He decides to rent a telescope for $\$ 50.00$ a week and charge his friends to use it to peep at the games for 30 seconds. He can act as a single-price monopolist for renting out "peeps." For each person who takes a 30 -second peep, it costs Jimmy $\$ 0.20$ to clean the eyepiece. This table shows the information Jimmy has gathered about the weekly demand for the service. a. For each price in the table, calculate the total revenue from selling peeps and the marginal revenue per peep. b. At what quantity will Jimmy's profit be maximized? What price will he charge? What will his total profit be? c. Jimmy's landlady complains about all visitors and tells him to stop selling peeps. But, if he pays her $\$ 0.20$ for every peep he sells, she won't complain. What effect does the $\$ 0.20$ -per-peep bribe have on Jimmy's marginal cost per peep? What is the new profit-maximizing quantity of peeps? What effect does the $\$ 0.20$ -per-peep bribe have on Jimmy's total profit?

Jimmy's room overlooks a major league baseball stadium. He decides to rent a telescope for $\$ 50.00$ a week and charge his friends to use it to peep at the games for 30 seconds. He can act as a single-price monopolist for renting out "peeps." For each person who takes a 30 -second peep, it costs Jimmy $\$ 0.20$ to clean the eyepiece. This table shows the information Jimmy has gathered about the weekly demand for the service.
a. For each price in the table, calculate the total revenue from selling peeps and the marginal revenue per peep.
b. At what quantity will Jimmy's profit be maximized? What price will he charge? What will his total profit be?
c. Jimmy's landlady complains about all visitors and tells him to stop selling peeps. But, if he pays her $\$ 0.20$ for every peep he sells, she won't complain. What effect does the $\$ 0.20$ -per-peep bribe have on Jimmy's marginal cost per peep? What is the new profit-maximizing quantity of peeps? What effect does the $\$ 0.20$ -per-peep bribe have on Jimmy's total profit?

Key Concepts

Marginal Cost

Marginal cost represents the extra cost incurred by producing one more unit of a service or product. In this scenario, it includes the variable cost per peep, such as the cleaning cost and any additional expenses like side payments. Understanding marginal cost is vital because it directly influences profit decisions and the determination of the optimal level of production.

Marginal Revenue

Marginal revenue is the additional revenue earned by selling one extra unit of a product or service. For a monopolist, marginal revenue typically falls as output increases due to the downward-sloping demand curve. Calculating marginal revenue from discrete data helps in identifying how revenue changes with each additional unit, which is critical for making optimal production decisions.

Profit Maximization

Profit maximization occurs when a firm produces to the point where the marginal revenue from selling an extra unit equals the marginal cost of producing that unit (MR = MC). This condition ensures that any additional unit produced would either add to or reduce overall profit, and thus represents the optimal decision-making point for a monopolist seeking to maximize profit.

Demand Analysis

Demand analysis involves examining the relationship between the price of a good or service and the quantity that consumers are willing to purchase. In this context, the demand schedule provides crucial information about how many 'peeps' are sold at different price points, which is essential for calculating total revenue and understanding consumer behavior in a monopolistic market.

Monopoly Pricing

Monopoly pricing refers to the strategy employed by a single seller in a market with no close substitutes for its product or service. A monopolist sets a single price for all customers rather than varying prices by customer. This approach simplifies decision-making since the monopolist’s output and pricing decisions are based on the available market demand and cost structure, aiming to maximize profits.

Total Revenue

Total revenue is the overall amount of money received from sales of a product or service, calculated by multiplying the price per unit by the number of units sold. Tracking total revenue across different price levels allows a firm to determine the income generated at various points on the demand curve and is a necessary step in profit analysis.

Transcript

00:02 Jimmy has rented a telescope for $50 a week, and he uses it to let his friends have 30 -second looks at a baseball game nearby.

00:13 It cost him 20 cents to clean the eyepiece after each person has their turn, and we want to know what's our total revenue and marginal revenue.

00:23 Our first two columns have the demand curve for the peeps.

00:28 To get total revenue, we multiply along our demand curve.

00:32 Price times quantity.

00:35 So if our price is 90 cents and we have 150 peeps, total revenue would be 90 cents times 150 would be $135.

00:46 And we know that marginal revenue is a change in total revenue that you get when you sell one more unit.

00:54 So if we look at an output of 100 when we were charging a dollar, our total revenue there is 100.

01:02 If we lower the price to 90 cents we'll sell 50 more peeps and our total revenue will be 135.

01:11 So my change in total revenue would be $35, but that's not for one peep.

01:18 That's for selling 50 more so we have to divide by 50 and that gives us a marginal revenue of 70 cents.

01:26 All the other marginal revenues are calculated in exactly the same way.

01:32 Then we want to know if the marginal cost is 20 cents per peak, what's my profit maximizing output? so my rule is to maximize profit produce as long as marginal revenue is greater than or equal to marginal cost.

01:51 So if my marginal revenue is 20 cents, that's true all the way up to an output of 250 and a price to sell 250 according to our demand curve, we should charge 70 cents a peep...

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