Problem 10 - Applied Calculus

Question

The marginal cost at a production level of 2000 units of an item is 810 per unit and the average cost of producing 2000 units is \(\$ 15\) per unit. If the production level were increased slightly above 2000 , would the following quantities increase or decrease, or is it impossible to tell? (a) Average cost (b) Profit

Step-by-Step Solution

Answer

(a) Average cost will increase. (b) Profit will decrease, assuming the selling price is less than $810.

Step 1: Understanding the Variables

First, identify the key details from the problem. The marginal cost (MC) at 2000 units is $810, and the average cost (AC) is $15 per unit at the same production level. We want to determine what happens to the average cost and profit if production increases slightly above 2000 units.

Step 2: Analyzing Average Cost

The average cost is calculated by dividing the total cost by the number of units produced. Since the marginal cost ($810 per unit) is higher than the average cost ($15 per unit), producing additional units at the marginal cost would increase the overall average cost per unit.

Step 3: Average Cost Conclusion

Since the marginal cost of producing additional units is higher than the current average cost, increasing production will cause the average cost to increase.

Step 4: Analyzing Profit

Profit is the difference between total revenue and total cost. If the price per unit sold remains constant, any addition in units produced with a marginal cost greater than the selling price will decrease the overall profit margins. Therefore, whether the profit increases or decreases depends on selling price.

Step 5: Profit Conclusion

With the marginal cost exceeding the average cost, unless the selling price of the item is greater than $810, any increase in production will likely decrease the profit, as costs will overshadow revenue gains.

Key Concepts

Understanding Average Cost

Average cost is a fundamental concept in economics. It refers to the cost incurred on average for each unit of production. You calculate it by dividing the total cost of production by the number of units produced. This gives an insight into the cost efficiency of operations.
In the scenario given, each of the 2000 units costs $15 on average. It's essential to compare it to the marginal cost — the cost of producing one more unit.
Here, the marginal cost is significantly higher at $810 per unit. When the marginal cost exceeds the average cost, producing additional units will lead to an increase in the average cost per unit. This is because each new unit adds more to the total cost than is offset by the spread of costs over a larger number of units.

• This relation can help businesses determine production levels that optimize cost efficiency.
• Understanding how marginal and average costs interact allows for strategic decision-making in production.

Analyzing Profit

Profit analysis is crucial for assessing the viability of increased production levels. Profit, in simple terms, is the total revenue minus total costs. It requires consideration of both fixed and variable costs and understanding how these costs affect revenue.
To increase profit, revenues need to rise faster than costs. In the provided scenario, profit depends on the selling price of the item compared to the marginal cost. If the selling price is less than the marginal cost of $810, increasing production may not be profitable.

• Even a slight increase in production may reduce profit if costs overshadow the revenue gained from additional sales.
• Therefore, a company's strategic goal should be to balance production so that the items produced are sold at a price exceeding their marginal costs, thereby optimizing profit margins.

Core Economic Principles

Economics helps us understand the intricate details of production and cost management. At its core, it focuses on how resources are used and distributed within markets. The concepts of marginal and average costs are fundamental in understanding economic efficiencies and diseconomies.
With marginal cost analysis, businesses can deduce when additional production becomes economically viable. If marginal costs exceed average costs, the law of diminishing returns may be at play, signaling inefficiency in production beyond a certain point.

• Economic theory aids in forecasting the impact of production adjustments on costs and revenues.
• By examining both average and marginal costs, companies can make informed decisions to enhance productivity and profitability.

Through this knowledge, businesses can make more informed decisions about scaling production up or down, ensuring sustainability and economic growth.