Question

Assume De Beers is the sole producer of diamonds. When it wants to sell more diamonds, it must lower its price in order to induce shoppers to buy more Furthermore, each additional diamond that is produced costs more than the previous one due to the difficulty of mining for diamonds. De Beers's total benefit schedule is given in the accompanying table, along with its total cost schedule. $$\begin{array}{ccc}\begin{array}{c} \text { Quantity of } \\\\\text { diamonds } \end{array} & \text { Total benefit } & \text { Total cost } \\ 0 & \$ 0 & \$ 0 \\\1 & 1,000 & 50 \\\2 & 1,900 & 100 \\\3 & 2,700 & 200 \\\4 & 3,400 & 400 \\\5 & 4,000 & 800 \\\6 & 4,500 & 1,500 \\\7 & 4,900 & 2,500 \\\8 & 5,200 & 3,800\end{array}$$ a. Draw the marginal cost curve and the marginal benefit curve and, from your diagram, graphically derive the optimal quantity of diamonds to produce. b. Calculate the total profit to De Beers from producing each quantity of diamonds. Which quantity gives De Beers the highest total profit?

Short answer

To find the optimal quantity, plot the marginal benefit (benefit of one additional unit) and marginal cost (cost of one additional unit) on a graph. The intersection is the optimal quantity. Calculate profit by subtracting total costs from total benefits; the quantity with the highest profit is optimal.

Step-by-step solution

Plotting the Marginal Benefit (MB) Curve

First, we need to determine the marginal benefit for each additional unit of diamonds sold. The marginal benefit is the increase in total benefit when one more unit is sold. To calculate the marginal benefit, subtract the total benefit of the previous quantity from the total benefit of the current quantity. Then plot these points on a graph to form the MB curve.

Plotting the Marginal Cost (MC) Curve

Secondly, we should calculate the marginal cost for each additional unit of diamonds produced. The marginal cost is the increase in total cost when one more unit is produced. To calculate the marginal cost, subtract the total cost of the previous quantity from the total cost of the current quantity. Then plot these points on a graph to form the MC curve.

Finding the Optimal Quantity of Diamonds to Produce Graphically

With both MB and MC curves on the same graph, identify the point where the MB curve intersects the MC curve. This is the equilibrium point representing the optimal quantity of diamonds to produce, as it's where the additional benefit of producing one more unit equals the additional cost of producing that unit.

Calculating Total Profit for Each Quantity of Diamonds

Calculate the total profit for each quantity by subtracting the total cost from the total benefit. The total profit at each quantity level is simply Total Benefit - Total Cost.

Determining the Quantity with the Highest Total Profit

Compare the total profits for all quantities. The highest total profit indicates the most profitable quantity for De Beers to produce.

Key concepts

Marginal Benefit

Marginal benefit is a critical concept in microeconomics, referring to the additional satisfaction or utility a consumer receives when one more unit of a product is consumed. To put it simply, it's the extra value that consumers place on having 'one more' of something.

For businesses like De Beers, understanding the marginal benefit helps in pricing and production decisions. It determines how much a consumer is willing to pay for each additional unit, which in the exercise, reflects the increasing total benefit from selling more diamonds. Marginal benefit decreases as consumption increases, a phenomenon known as the law of diminishing marginal utility.

By calculating the difference in total benefits as more units are sold, De Beers can identify how the consumers' willingness to pay changes. When plotted on a graph, the marginal benefit curve typically slopes downwards, illustrating that each additional unit is valued less than the previous one.

Marginal Cost

Marginal cost holds immense importance in the domain of microeconomics, especially for producers. It represents the cost of producing one additional unit of a good or service. In the example of De Beers, each extra diamond that is mined costs more than the last, illustrating a key property of marginal cost – it can increase as production increases, often due to factors such as the limited availability of resources or the increased effort required to produce additional units.

For producers, marginal cost helps in deciding the optimal level of production. The marginal cost curve is typically upward sloping, indicating higher costs for additional production. This can be seen in the step-by-step solution which plots the marginal cost for each additional diamond produced. Optimal production decisions are made where marginal cost intersects with marginal benefit, indicating a balance between the cost of production and the value it brings to consumers.

Optimal Production Quantity

The optimal production quantity is a vital economic decision point for producers like De Beers. It refers to the quantity of goods a firm should produce to maximize its profit, balancing the marginal cost and marginal benefit.

In our exercise, we can determine the optimal production quantity by finding the intersection of the marginal cost and marginal benefit curves on a graph. This intersection represents the equilibrium where the additional revenue from selling one more diamond equals the additional cost of producing it. Producing more than this quantity would result in higher costs than benefits, while producing less would mean missing out on potential profits.

As illustrated in the steps provided, by plotting the marginal curves and identifying their intersection point, De Beers can visually discern the most advantageous production level. This level of production maximizes the firm's benefits without incurring disproportionate costs.

Total Profit Calculation

Total profit calculation is an indispensable tool for any business aiming to evaluate its financial performance. Profit is essentially the lifeblood of a company, providing the resources needed for growth, investment, and reward to shareholders.

In microeconomic terms, total profit is the difference between total benefit (revenue) and total cost incurred in the production of goods. Using the example from our textbook, De Beers's total profit at each quantity can be determined by subtracting the total cost from the total benefit. This calculation shows how profit changes as the quantity of production varies.

The solution process takes this a step further by comparing total profits at each quantity to ascertain which quantity maximizes profit. This approach involves listing the total benefits and costs for producing different quantities of diamonds and deriving the profits from these pairs of values. It is a straightforward yet potent means to pinpoint the pinnacle of profitability for De Beers.