2. A company is considering building a bridge across a river. The bridge would cost $2 million to build and nothing to maintain. The following table shows the company¡¯s anticipated demand over the lifetime of the bridge:
Price per crossing ($) 8 7 6 5 4 3 2 1 0
Number of crossings (¡®000) 0 100 200 300 400 500 600 700 800
a. If the company were to build the bridge, what would be its profit-maximizing price? Would that be the efficient level of output? Why or why not?
b. If the company is interested in maximizing profit, should it build the bridge? What would be its profit or loss?
c. If the government were to build the bridge, what price should it charge?
d. Should the government build the bridge? Explain your answer.
a. The company's profit-maximizing price would be $6 per crossing. This would not be the efficient level of output, as the efficient level of output would be the price that would equate the marginal cost of production with the marginal benefit of production. In this case, the marginal cost of production is zero, so the efficient level of output would be the price that would equate the marginal benefit of production with zero.
b. If the company is interested in maximizing profit, it should build the bridge. The company's profit would be $2.4 million.
c. If the government were to build the bridge, it should charge a price that would equate the marginal cost of production with the marginal benefit of production. In this case, the marginal cost of production is zero, so the price should be set at zero.
d. The government should build the bridge if the benefits of the bridge outweigh the costs. This can be determined by comparing the total benefits of the bridge to the total costs of the bridge. If the total benefits exceed the total costs, then the government should build the bridge.
a. To find the profit-maximizing price, we need to analyze the data provided in the table. The profit for each level of output can be calculated by subtracting the cost of building the bridge ($2 million) from the revenue generated at each price level, which is the product of the price per crossing and the number of crossings.
Price per crossing: [$8, $7, $6, $5, $4, $3, $2, $1, $0]
Number of crossings: [0, 100, 200, 300, 400, 500, 600, 700, 800]
Profit: [0, $500, $1,000, $1,500, $2,000, $2,500, $3,000, $3,500]
The profit-maximizing price occurs at the price level that generates the highest profit. Looking at the profit values, we can see that the highest profit ($3,500) occurs at a price of $0.
The efficient level of output is the level at which marginal cost equals marginal benefit. To determine if the profit-maximizing price also leads to an efficient level of output, we would need information about the marginal cost and marginal benefit associated with each level of output. However, since this information is not provided, we cannot definitively determine if the profit-maximizing price corresponds to the efficient level of output.
b. To determine if the company should build the bridge, we need to compare the profit it would earn from building the bridge to the cost of building it.
Since the profit-maximizing price is $0, the company would not generate any revenue and would make a loss equal to the cost of building the bridge ($2 million). Therefore, the company should not build the bridge if its goal is to maximize profit.
c. If the government were to build the bridge, it would need to consider the social welfare and pricing strategies that align with that goal. The government would have to decide on a price that maximizes social welfare, which can include factors such as accessibility, affordability, and overall economic impact.
However, without further information on the government's goals and considerations, it is impossible to determine the specific price the government should charge for crossing the bridge.
d. Whether or not the government should build the bridge depends on the overall welfare and economic considerations of the society. Factors such as the demand for crossing the river, the potential benefits to the community (e.g., improved transportation, economic development), and the cost of building the bridge need to be assessed.
If the benefits outweigh the costs and the bridge construction aligns with the government's goals and priorities, then the government may decide to build the bridge. However, without additional information, it is impossible to make a definitive decision on whether the government should build the bridge.
To find the profit-maximizing price for the company, we need to analyze the demand and cost data provided. The demand table shows the relationship between the price per crossing and the corresponding number of crossings. The cost of building the bridge is given as $2 million, and there are no maintenance costs.
a. Profit can be calculated as Total Revenue (TR) minus Total Cost (TC). To find the profit-maximizing price, we first need to calculate the total revenue for each price level. Total revenue equals the price per crossing multiplied by the number of crossings. Then, we subtract the total cost of building the bridge from the total revenue to find the profit.
To calculate the profit for each price level:
Price 8: TR = 8 (1000) = $8000 | Profit = TR - $2 million
Price 7: TR = 7 (1000) = $7000 | Profit = TR - $2 million
Price 6: TR = 6 (1000) = $6000 | Profit = TR - $2 million
Price 5: TR = 5 (1000) = $5000 | Profit = TR - $2 million
Price 4: TR = 4 (1000) = $4000 | Profit = TR - $2 million
Price 3: TR = 3 (1000) = $3000 | Profit = TR - $2 million
Price 2: TR = 2 (1000) = $2000 | Profit = TR - $2 million
Price 1: TR = 1 (1000) = $1000 | Profit = TR - $2 million
Price 0: TR = 0 (1000) = $0 | Profit = TR - $2 million
The table of profits for each price level would be:
Price ($) | Profit ($)
8 | - $1,992,000
7 | - $1,993,000
6 | - $1,994,000
5 | - $1,995,000
4 | - $1,996,000
3 | - $1,997,000
2 | - $1,998,000
1 | - $1,999,000
0 | - $2,000,000
From the table of profits, we can observe that increasing the price leads to a decrease in total revenue, resulting in greater losses. However, at the price of $0, there are no costs associated with each crossing, so the company would not incur any losses. Despite having no costs, setting the price at $0 would also result in no profit. Hence, the profit-maximizing price for the company would be $0 as it minimizes losses.
Whether this is the efficient level of output depends on the concept of allocative efficiency. Allocative efficiency occurs when production aligns with consumer preferences, meaning that resources are being allocated in a way that maximizes overall welfare. In this scenario, setting the price at $0 might result in excess demand due to the high consumer surplus, which implies that the bridge is underutilized. Therefore, in terms of allocative efficiency, setting the price at $0 may not be the most efficient level of output.
b. If the company is interested in maximizing profit, it should compare the profit at the chosen price level with the cost of building the bridge. Since the profit-maximizing price is $0, the company would not be able to cover the cost of building the bridge, resulting in a loss of $2 million.
c. If the government were to build the bridge, it may have different objectives than profit maximization, such as social welfare or revenue generation. To determine the price the government should charge, it should consider the cost of building the bridge and the demand for bridge crossings. The government could analyze the willingness to pay for bridge crossings by surveying potential users or conducting market research to determine an appropriate price. Additionally, the government might consider the economic benefits, such as reduced travel time and increased accessibility, provided by the bridge when setting the price.
d. Whether the government should build the bridge depends on various factors, such as the cost of construction, expected demand, potential economic benefits, and overall societal welfare. The decision requires considering both the financial viability and the potential positive externalities associated with the bridge project. It is beyond the scope of this explanation to determine whether the government should build the bridge as it involves subjective judgments and policy considerations.