Question

After mining 9,273 tons of coal, Blue Sky Mining's managers note that the marginal cost of mining the next ton of coal would be \(\$ 40\) per ton. They also calculate that the user cost of mining that next ton of coal would be \(\$ 35 .\) If the market price of coal is S72, should Blue Sky mine an additional ton of coal? a. Yes. b. No. c. More information is needed.

Short answer

b. No, the total cost of \$75 is greater than the market price of \$72.

Step-by-step solution

Understand the Given Information

Blue Sky Mining has already mined 9,273 tons of coal. The marginal cost of mining another ton is given as $40/ton. The user cost for the next ton is $35, and the market price for coal is $72.

Calculate the Total Cost of Mining the Next Ton

The total cost of mining another ton includes both the marginal cost and the user cost. Therefore, the total cost of mining the next ton is\[\text{Total Cost} = \text{Marginal Cost} + \text{User Cost} = 40 + 35 = 75.\]

Compare Total Cost with Market Price

Now, compare the total cost of mining the next ton to the market price.If:\[\text{Market Price} = 72 < 75 = \text{Total Cost},\]then the total cost of mining the next ton exceeds the market price.

Conclude Based on Comparison

Since the total cost (\\(75) is greater than the market price (\\)72), it is not profitable for Blue Sky Mining to mine an additional ton of coal.

Key concepts

User Cost

The concept of user cost is essential in the assessment of whether to undertake an additional output or not. User cost represents the value of future opportunities forfeited when a resource is used today. In the context of mining, it involves understanding how utilizing the coal now might limit future profits or opportunities. Users have to consider this cost because it is not only about extracting and selling a resource, but also about the long-term impact and the potential depletion of the resource, which could affect future production cost or scarcity of that resource.

• Understanding User Cost: For Blue Sky Mining, mining an additional ton of coal means giving up potential future profits if the cost of coal rises.
• Calculation: In this scenario, the user cost is listed at $35 per ton, representing the long-term impact on resource availability and future profit opportunities.

The inclusion of user cost in decision-making ensures that short-term gains do not overshadow long-term sustainability and profitability.

Market Price

Market price refers to the amount that a buyer is willing to pay for a commodity in an open market. It reflects the equilibrium established by demand and supply dynamics and is central in investment and production decisions. When evaluating whether to extract additional resources, businesses must consider if the market price justifies the total costs involved in production, including both marginal and user costs.

• Importance of Market Price: In Blue Sky Mining's case, the market price for coal is $72 per ton.
• Influence on Decision-Making: Market price directly impacts whether mining additional coal is profitable; it must exceed the sum of all costs associated.

If the total costs exceed the market price, as in this case, it implies a loss for the miner, suggesting no additional mining should occur unless market conditions improve.

Total Cost

Total cost is the comprehensive expense involved in producing a certain quantity of goods. It includes various costs incurred, such as fixed, variable, marginal, and user costs. The total cost for producing the next unit is vital for organizations in deciding production levels, especially when market price needs to be considered against these costs.

• Components of Total Cost: The key is understanding components such as marginal cost and user cost. For Blue Sky Mining, the total cost of mining the next ton is calculated as $40 (marginal) + $35 (user) = $75.
• Decision Criterion: Total cost plays a pivotal role; when it exceeds the market price, continuing production for additional units might not be cost-effective.

For Blue Sky Mining, since the total cost of $75 per ton surpasses the market price of $72 per ton, it suggests not mining the additional ton to avoid losses.