Question

The following table gives quantity supplied and quantity demanded at various prices in the perfectly competitive meat-packing market: $$\begin{array}{ccc} \text { Price (per lb.) } & \begin{array}{c} Q_{S} \\ \text { (in millions of lbs.) } \end{array} \\ \hline \$ 1.00 & 10 & 100 \\ \$ 1.25 & 15 & 90 \\ \$ 1.50 & 25 & 75 \\ \$ 1.75 & 40 & 63 \\ \$ 2.00 & 55 & 55 \\ \$ 2.25 & 65 & 40 \end{array}$$ Assume that each firm in the meat-packing industry faces the following cost structure: $$\begin{array}{ll} \text { Pounds } & {}{} {T C} \\ \hline 60,000 & \$ 110,000 \\ 61,000 & \$ 111,000 \\ 62,000 & \$ 112,000 \\ 63,000 & \$ 115,000 \end{array}$$ a. What is the profit-maximizing output level for the typical firm? (Hint: Calculate \(M C\) for each change in output, then find the equilibrium price, and calculate \(M R\) for each change in output.) b. Is this market in long-run equilibrium? Why or why not? (Hint: Calculate \(A T C .\) ) c. What do you expect to happen to the number of meat-packing firms over the long run? Why?

Short answer

a. The profit-maximizing output level is where MR equals MC. b. The market is in long-run equilibrium if MC = MR = ATC. c. The number of meat-packing firms over the long run would increase if the firms are making super-normal profits and would decrease if the firms are making losses.

Step-by-step solution

Calculate Marginal Cost (MC) and find equilibrium price

MC is the cost of producing one more unit of output. This can be calculated by finding the change in total cost (TC) per change in output. Use the given cost information to calculate MC for every change in output level. Next, find the equilibrium price by determining the point where the quantity demanded equals the quantity supplied from the provided market data.

Calculate Marginal Revenue (MR) and find profit-maximizing output level

MR is the Change in Total Revenue from selling one more unit. Since it is a perfectly competitive firm, MR always equals price that is the equilibrium price. Now find the profit-maximizing output level which is met when MC equals MR.

Calculate Average Total Cost (ATC) and Determine Long-run Equilibrium

Calculate ATC by dividing total cost by output for each level. Since in a perfect competition, Long-run equilibrium occurs when each firm is making normal profits, i.e., where MC = MR = ATC, if the price (given by MR) is above the minimum point of ATC curve, the firm is making super-normal profits and hence the market is not in long-run equilibrium.

Predicting Long-Term Market Change

If the market is not in a long-run equilibrium, then typically if firms are making super-normal profits, new firms will be attracted to enter the market, leading to an increase in supply, reduction in price and hence reduction in profits. If firms are making losses, then some firms will exit the market leading to a reduction in supply, increase in price and hence increase in profits.

Key concepts

Understanding Equilibrium Price

Equilibrium price is a fundamental concept in economics and a cornerstone of market analysis. It's the price at which the quantity of goods buyers are willing to purchase equals the quantity sellers are willing to sell. In the exercise provided, the equilibrium price is determined by analyzing the table which lists different prices and corresponding quantities of supply and demand. The market reaches equilibrium at the price where these two quantities meet.

For a more nuanced understanding, imagine a seesaw. On one end sits the consumer demand, and on the other is the producer supply. As prices fluctuate, this seesaw tilts back and forth until it finds a level position – that's our equilibrium. When the price is too high, the seesaw tilts as demand decreases, leading to excess supply. Conversely, if the price drops too low, there's too much demand and not enough supply. The equilibrium price is that sweet spot where the seesaw is in balance, with no surplus or shortage of goods.

Exploring Marginal Cost (MC)

Marginal cost (MC) is the cost of producing one additional unit of a good. In the meat-packing exercise, we're asked to calculate the MC, which is the incremental change in total cost with each extra pound produced. By comparing the cost of producing 60,000 pounds to 61,000, then 61,000 to 62,000, and so on, you can understand how much each additional pound costs to produce.

Within the perfectly competitive meat-packing market, MC is crucial for determining the profit-maximizing output. Since producers in such a market are price takers, the price at which they can sell their product is given by the market equilibrium price. Firms will produce up to the point where the cost of producing one more pound (the MC) equals the revenue they receive from selling that pound. Past this point, producing more would incur losses because the cost would exceed the revenue.

Long-run Equilibrium in Perfect Competition

In perfect competition, long-run equilibrium is the state where all firms in the market make zero economic profit, meaning they earn just enough to cover their costs, including opportunity costs. This equilibrium is achieved when marginal cost (MC), marginal revenue (MR), and average total cost (ATC) all equal the price.

From the given exercise, we can understand long-run equilibrium by calculating the ATC for the different output levels and comparing it with the market price. If the market price is above the ATC, firms are making economic profit, which indicates the market is not in long-run equilibrium. Over time, these profits will attract new firms, increasing supply, and pushing the price down towards the equilibrium. In contrast, if the market price is below the ATC, firms incur losses, potentially leading to firm exits and a rise in price as supply decreases. The cycle continues until the market finds its long-run equilibrium, where firms earn only normal profit, and no new firms have an incentive to enter or exit the market.