Consider total cost and total revenue given in the following table: $$\begin{array}{lcccccccc}\text { Quantity } & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\\\\text { Total cost } & \$ 8 & 9 & 10 & 11 & 13 & 19 & 27 & 37 \\\\\text { Total revenue } & \$ 0 & 8 & 16 & 24 & 32 & 40 & 48 & 56\end{array}$$ a. Calculate profit for each quantity. How much should the firm produce to maximize profit? b. Calculate marginal revenue and marginal cost for each quantity. Graph them. (Hint: Put the points between whole numbers. For example, the marginal cost between 2 and 3 should be graphed at \(21 / 2 .\).) At what quantity do these curves cross? How does this relate to your answer to part (a)? c. Can you tell whether this firm is in a competitive industry? If so, can you tell whether the industry is in a long-run equilibrium?

Step by step solution

01

Calculate Profit for Each Quantity

To find the profit for each quantity, subtract the total cost from the total revenue for each corresponding quantity level.

02

Determine the Quantity Maximizing Profit

Examine the profit at each quantity and identify the point at which profit is maximized. This is where profit cannot be increased by producing more or less.

03

Calculate Marginal Revenue for Each Quantity

Marginal Revenue (MR) is the change in total revenue from selling one additional unit. Calculate MR for each increase in quantity, specifically between each pair of adjacent quantities.

04

Calculate Marginal Cost for Each Quantity

Marginal Cost (MC) is the change in total cost from producing one additional unit. Calculate MC for each increase in quantity, similarly to MR, using the differences in total cost between adjacent quantities.

05

Graph Marginal Revenue and Marginal Cost

Plot MR and MC points on a graph between the whole numbers, with quantity on the x-axis and MR and MC on the y-axis. Connect the points to form the MR and MC curves.

06

Find the Quantity Where MR and MC Curves Cross

Observe the point where MR and MC intersect on the graph. This point indicates the optimal production quantity in traditional microeconomic theory.

07

Analyze Industry Type and Equilibrium

Consider whether the MR curve is constant and whether MC equals MR at the highest profit. A constant MR implies a competitive market. If the firm is earning zero economic profit, it suggests long-run equilibrium.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Total Cost and Revenue

Understanding the relationship between total cost and total revenue is crucial in microeconomics. Total cost represents the complete cost of production which includes both fixed and variable costs, while total revenue is the total income received from selling goods or services. By examining these figures, businesses can assess their profitability at different levels of production.

For instance, using the provided exercise, the profit at each quantity can be calculated by subtracting the total cost from the total revenue for that quantity. A simple illustration: at a quantity of 2, the total cost is \(10 and the total revenue is \)16, hence the profit is \(16 - \)10 = $6. Repeat this for all quantities to understand how revenues and costs change with production levels.

Profit Maximization

Profit maximization is the process by which a firm determines the price and output level that returns the greatest profit. To achieve this, one must analyze the profits at various production levels to pinpoint the quantity where the profit is at its peak. This does not only rely on the highest total revenue but must also consider the associated total costs.

In the exercise scenario, you would look for the point at which profit (total revenue minus total cost) cannot be increased by producing and selling more or fewer units. Let's say, upon calculation, that maximum profit occurs at a quantity of 5 units. Producing more than this amount would begin to reduce the overall profit due to increasing costs outpacing revenue.

Marginal Revenue and Cost

Marginal revenue (MR) and marginal cost (MC) are two pivotal concepts in microeconomics that help explain how a company decides on the optimal level of output. Marginal revenue represents the additional income from selling one more unit of a good or service, while marginal cost is the additional cost of producing one extra unit.

In practical terms, a business examines changes in total revenue and total cost when an extra unit is sold or produced, respectively. Graphing these trends aids in visualizing the relationship between output levels and profitability. The intersection of MR and MC curves typically signifies the optimal output level for profit maximization, as it represents the point where the cost of producing an additional unit equals the revenue it generates.

Competitive Market Analysis

A competitive market analysis involves evaluating the environment in which a firm operates. Fundamental indicators include the nature of the marginal revenue curve and the market's pricing power. In a purely competitive market, the MR curve is horizontal, signifying that a firm can sell as much as it wants at the market price but cannot influence the price itself.

From our exercise, if the MR remains constant as quantity increases, it suggests that the firm is a price taker in a competitive market. However, if the firm can influence the price, the MR curve would slope downwards, and the market structure could be monopolistic or oligopolistic. Identifying these market traits can greatly assist in strategic decision-making.

Long-Run Equilibrium

In the context of microeconomics, long-run equilibrium occurs when firms in an industry are earning zero economic profit - this doesn't mean they aren't making money, but rather that they're making just enough to cover their opportunity costs. This situation occurs when the market price stabilizes so that the average total cost equals the marginal revenue.

Referring to our exercise, a firm would be in long-run equilibrium if the quantity produced and sold at the point where MR crosses MC results in no economic profit. This balance suggests that the resources in the industry are being used efficiently, and there’s no incentive for other firms to enter or exit the market.