Question

Hot Air Balloon Rides is a single-price monopoly. Columns 1 and 2 of the table set out the market demand schedule and columns 2 and 3 set out the total cost schedule. $$\begin{array}{ccc} \begin{array}{c} \text { Price } \\ \text { (dollars } \\ \text { per ride } ) \end{array} & \begin{array}{c} \text { Quantity } \\ \text { (rides } \\ \text { per month) } \end{array} & \begin{array}{c} \text { Total cost } \\ \text { (dollars } \\ \text { per month) } \end{array} \\ \hline 220 & 0 & 80 \\ 200 & 1 & 160 \\ 180 & 2 & 260 \\ 160 & 3 & 380 \\ 140 & 4 & 520 \\ 120 & 5 & 680 \end{array}$$ If instead of taxing Hot Air's profit, the government imposes a sales tax on balloon rides of \(\$ 30\) a ride, what are the new profit-maximizing quantity, price, and economic profit?

Short answer

The new profit-maximizing quantity is 2 rides, the price is \(180, and the economic profit is \)100.

Step-by-step solution

Identify Market Demand and Cost Schedules

Extract the data from the table for price, quantity, and total cost. The market demand schedule expresses the relationship between the quantity of rides (Q) and the price per ride (P). The total cost schedule corresponds to the total cost C for producing Q rides per month.

Determine Marginal Revenue (MR) and Marginal Cost (MC)

Calculate the Marginal Revenue (MR) and the Marginal Cost (MC) for each level of output. MR = Change in Total Revenue (TR) / Change in Quantity (Q)MC = Change in Total Cost (TC) / Change in Quantity (Q)TR = P * Q. Calculate each using Q=0: TR=0; Q=1: TR=200; ... up to Q=5.

Include Sales Tax in Cost

Since the government imposes a sales tax of \(30 per ride, adjust the cost schedule to include this tax for each quantity level. For example, TC at Q=1 with tax = Original TC + (Q * \)30) = 160 + 30 = 190

Identify New Marginal Cost with Tax

Adjust the Marginal Cost (MC) calculations to include the sales tax. For example, the new MC for Q=1 (with tax) = (new TC at Q=1 - new TC at Q=0) / 1.

Find Profit-Maximizing Output

Determine the output level where Marginal Revenue (MR) equals the new Marginal Cost (MC), MR = MC. This is the profit-maximizing quantity after considering the tax.

Determine the Price and Economic Profit

At the profit-maximizing quantity level, refer back to the demand schedule to determine the corresponding price. Calculate the economic profit by subtracting the new total cost from the total revenue at this quantity level.

Key concepts

Marginal Revenue

Marginal Revenue (MR) is crucial in understanding how a monopoly makes decisions. It represents the additional revenue gained from selling one more unit of a good or service. In our exercise, Hot Air Balloon Rides must first know how much more they earn with each additional ride. To do this, we calculate Total Revenue (TR) by multiplying price (P) and quantity (Q). For example, when Q=1, TR is 200 (since 200 * 1 = 200). Now, MR is the change in TR as quantity changes. So, if TR at Q=2 is 360, MR when moving from Q=1 to Q=2 is (360 - 200) / 1 = 160. This helps us know how much extra money is earned with each additional ride taken.

Marginal Cost

Marginal Cost (MC) shows how much extra it costs to produce one more ride. It helps us understand production costs at different output levels. In our scenario, we calculate MC by finding the change in total cost (TC) divided by the change in quantity (Q). For instance, if TC goes from 80 (at Q=0) to 160 (at Q=1), the MC is (160 - 80) / 1 = 80. Calculating MC at each level helps Hot Air Balloon Rides decide how much to produce. When MC equals MR, that's where profit maximization happens.

Economic Profit

Economic Profit is the difference between total revenue (TR) and total cost (TC), adjusted for opportunity costs. It’s different from accounting profit, which just subtracts explicit costs from revenue. In this exercise, TR is derived from selling the rides, while TC includes all production costs. By subtracting TC from TR, we get economic profit. For instance, if TR at Q=3 is 480 and TC is 380, then the economic profit is 480 - 380 = 100. This profit shows the real financial health of a business and is a vital indicator for decision-making.

Sales Tax Impact

Sales Tax imposes additional costs on each unit sold. In the exercise, a $30 tax is added per ride, affecting overall costs and marginal costs. This means the new total cost (TC) includes the tax. For example, at Q=1, original TC is 160, and with tax, it becomes 160 + 30 = 190. The new Marginal Cost (MC) includes this extra tax amount. This increases the overall cost and impacts the profit-maximizing output level, as businesses have to adjust prices and quantities to accommodate the tax.

Profit Maximization

Profit Maximization is about finding the right balance where Marginal Revenue (MR) equals Marginal Cost (MC). This is the quantity where profits are highest. For Hot Air Balloon Rides, after including the sales tax, we determine where the new MC equals MR. Suppose MR=110 at a certain output level, and the new MC is also 110; that’s the optimal quantity. At this quantity, the demand schedule tells us the price. By selling at this price, economic profit is maximized, factoring in the new costs due to the tax. This helps businesses to strategize effectively and remain profitable.