Question

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? $$\begin{array}{c|c}\text { Price of } & \text { Quantity of } \\ \text { peep } & \text { peeps demanded } \\\\\ 1.20 & 0 \\\1.00 & 100 \\ 0.90 & 150 \\\0.80 & 200 \\\0.70 & 250 \\\0.60 & 300 \\\0.50 & 350 \\\0.40 & 400 \\\0.30 & 450 \\\0.20 & 500 \\ 0.10 & 550\end{array}$$

Short answer

With each peep originally costing Jimmy \)0.20 for cleaning, he maximizes profit where MR equals MC; after the landlady's complaint, the MC increases to $0.40 due to the bribe, affecting the profit-maximizing quantity and reducing total profit.

Step-by-step solution

Calculate Total Revenue (TR) for Each Price

To calculate the total revenue (TR) for each price, multiply the price per peep by the quantity of peeps demanded at that price. The formula for total revenue is TR = Price × Quantity.

Calculate Marginal Revenue (MR) per Peep

Marginal revenue (MR) is the increase in total revenue that results from selling one additional unit of a good or service. It can be calculated by taking the change in total revenue divided by the change in quantity. For the first quantity, MR is the same as the price because no previous data exists.

Identify Profit-Maximizing Quantity and Price

To find the profit-maximizing quantity, look for the quantity where MR equals marginal cost (MC). Since the MC is \(0.20 per peep, find the quantity where the MR from selling one more peep is \)0.20. Calculate profit by subtracting the total cost from total revenue. The total cost is the sum of the fixed cost of renting the telescope (\(50.00) and the variable cost of cleaning the eyepiece (\)0.20 per peep). The price Jimmy will charge is the price that corresponds to the profit-maximizing quantity on the demand table.

Calculate the Effect of the \(0.20-per-Peep Bribe on MC

The \)0.20 per peep bribe to the landlady increases Jimmy's marginal cost from \(0.20 to \)0.40 per peep since the cleaning cost and the bribe add up. This means for every peep sold, Jimmy's cost increases by \(0.40.

Find New Profit-Maximizing Quantity and Effect on Profit

With the new MC of \)0.40 per peep due to the bribe, the profit-maximizing quantity is where MR equals \(0.40. Calculate the new profit by subtracting the increased total cost (including the bribes) from the total revenue. The effect on Jimmy's total profit will be a reduction by the amount of the bribes paid.

Key concepts

Marginal Revenue

Marginal revenue (MR) is a crucial concept when it comes to understanding monopoly profit maximization. It refers to the additional income that a firm receives from selling one more unit of a good or service. In simpler terms, it's the increase in total revenue when one extra 'peep' is sold in our given scenario with Jimmy. To calculate MR, you observe the change in total revenue and divide it by the change in quantity sold.

Breaking it down further, if Jimmy sells one more 'peep' and his total revenue goes up by \(1.00, the marginal revenue for that extra peep is \)1.00. What's interesting in a monopoly is that the MR eventually starts to decrease as the quantity sold increases, because the monopolist must lower the price to sell more units. This price reduction affects the revenue obtained from selling previous units, thus changing the MR with each additional unit sold.

Marginal Cost

Another piece of the puzzle is the marginal cost (MC), which represents the cost of producing one additional unit of a product. In our case study, it was initially \(0.20 to clean the eyepiece for each additional 'peep' sold by Jimmy. When your monopoly – in this case, Jimmy's 'peep' selling business – is deciding how many units to sell, the goal is to produce up to the point where MR equals MC.

After Jimmy’s landlady demands a \)0.20 per peep as a bribe, the MC for Jimmy's service doubles. Now, for each peep, he must consider both the cleaning cost and the bribe, which in turn affects his profit-maximizing decision. The new MC affects how much he should sell to maximize profits since it changes the point where MR equals MC. This demonstrates that any change in the cost structure, like the bribe, directly impacts the optimal level of output and pricing strategy.

Total Revenue

Total revenue (TR) is the total income that a firm receives from selling its goods or services. For monopolies like Jimmy's 'peep' service, calculating TR is straightforward–it is the price of the good multiplied by the quantity sold. In the initial task, you see how to calculate TR by multiplying the price at each quantity level by the number of units sold at that price.

To maximize profits, a monopolist needs to consider how TR behaves in relation to changes in price and quantity. As Jimmy adjusts his prices, he'll observe changes in his total revenue. With each price adjustment that he makes, he'll serve a different number of 'peeps,' which will affect his TR differently. This interplay of price, quantity, and revenue is key to finding the sweet spot for profit maximization.

Demand Curve

The demand curve is a graphical representation of the quantity of a good that buyers are willing to purchase at various prices. For Jimmy's telescope 'peep' show, the demand curve would slope downward, indicating that at lower prices, a greater quantity of 'peeps' is demanded. Monopolists like Jimmy face a downward-sloping demand curve, meaning they must lower their price to sell more units.

In real-world monopolies, analyzing the demand curve helps determine the pricing strategy to maximize profits. The demand curve is essential for understanding how price changes affect the quantity demanded and, by extension, the total revenue and profit. When instructing on this topic, it's vital to help students visualize and understand that each price point on the demand curve corresponds to a specific quantity demanded, which affects a monopolist's decisions about pricing and the number of units to sell.