Assume De Beers is the sole producer of diamonds. When it...

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. $$ \begin{array}{|ccc|} \hline \begin{array}{c} \text { Quantity of } \\ \text { diamonds } \end{array} & \text { Total benefit } & \text { Total cost } \\ \hline 0 & \$ 0 & \$ 0 \\ 1 & 1,000 & 50 \\ 2 & 1,900 & 100 \\ 3 & 2,700 & 200 \\ 4 & 3,400 & 400 \\ 5 & 4,000 & 800 \\ 6 & 4,500 & 1,500 \\ 7 & 4,900 & 2,500 \\ 8 & 5,200 & 3,800 \\ \hline \end{array} $$ 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?

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.
$$
\begin{array}{|ccc|}
\hline \begin{array}{c}
\text { Quantity of } \\
\text { diamonds }
\end{array} & \text { Total benefit } & \text { Total cost } \\
\hline 0 & \$ 0 & \$ 0 \\
1 & 1,000 & 50 \\
2 & 1,900 & 100 \\
3 & 2,700 & 200 \\
4 & 3,400 & 400 \\
5 & 4,000 & 800 \\
6 & 4,500 & 1,500 \\
7 & 4,900 & 2,500 \\
8 & 5,200 & 3,800 \\
\hline
\end{array}
$$
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?

Key Concepts

Marginal Cost

Marginal cost refers to the additional cost incurred from producing one extra unit of output. In microeconomics, it is crucial because it helps determine the optimal level of production. As more units are produced, increasing marginal costs due to factors like resource scarcity or rising difficulty in production indicate when further production becomes less efficient.

Marginal Benefit

Marginal benefit is the additional benefit or revenue gained from producing one more unit of output. It is essential for decision making because comparing marginal benefit to marginal cost allows producers to determine the point at which producing additional units no longer increases overall profit. In many contexts, the marginal benefit curve can indicate consumers’ willingness to pay for additional units.

Profit Maximization

Profit maximization is the process of determining the output level at which total profit is the highest. In microeconomics, this is achieved by equating marginal cost with marginal benefit (or marginal revenue). When additional production results in a marginal cost higher than the marginal benefit, it signals that the optimal production quantity has been exceeded.

Graphical Analysis in Economics

Graphical analysis involves plotting marginal cost and marginal benefit curves to visually determine the optimal production level. The intersection of these curves represents the equilibrium where every additional unit produced would add as much cost as benefit. This technique is widely used to illustrate economic principles like efficiency and optimal resource allocation.

Total Profit Calculation

Total profit is calculated by subtracting total cost from total benefit (or total revenue). Analyzing total profit across different levels of production helps identify the production quantity that yields the highest profit. This concept is fundamental in economic decision making as it encompasses all revenues and costs associated with production.

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