Question

Assume the following cost data are for a purely competitive producer: $$\begin{array}{ccccc} \hline \begin{array}{c} \text { Total } \\ \text { Product } \end{array} & \begin{array}{c} \text { Average } \\ \text { Fixed cost } \end{array} & \begin{array}{c} \text { Average } \\ \text { Variable cost } \end{array} & \begin{array}{c} \text { Average } \\ \text { Total cost } \end{array} & \begin{array}{c} \text { Marginal } \\ \text { cost } \end{array} \\ \hline 0 \\ 1 & \$ 60.00 & \$ 45.00 & \$ 105.00 & \$ 45 \\ 2 & 30.00 & 42.50 & 72.50 & 40 \\ 3 & 20.00 & 40.00 & 60.00 & 35 \\ 4 & 15.00 & 37.50 & 52.50 & 30 \\ 5 & 12.00 & 37.00 & 49.00 & 35 \\ 6 & 10.00 & 37.50 & 47.50 & 40 \\ 7 & 8.57 & 38.57 & 47.14 & 45 \\ 8 & 7.50 & 40.63 & 48.13 & 55 \\ 9 & 6.67 & 43.33 & 50.00 & 65 \\ 10 & 6.00 & 46.50 & 52.50 & 75 \\ \hline \end{array}$$ a. At a product price of $\$ 56,$ will this firm produce in the short run? Why or why not? If it is preferable to produce, what will be the profit-maximizing or loss-minimizing output? Explain. What economic profit or loss will the firm realize per unit of output? b. Answer the relevant questions of 4 a assuming product price is $\$ 41$ c. Answer the relevant questions of 4 a assuming product price is $\$ 32$ d. In the table below, complete the short-run supply schedule for the firm (columns 1 and 2 ) and indicate the profit or loss incurred at each output (column 3). $$\begin{array}{cccc} \hline \begin{array}{c} \text { (1) } \\ \text { Price } \end{array} & \begin{array}{c} \text { (2) } \\ \text { Quantity } \\ \text { Supplied, } \\ \text { Single Firm } \end{array} & \begin{array}{c} \text { (3) } \\ \text { Profit }(+) \\ \text { or Loss }(-) \end{array} & \begin{array}{c} \text { (4) } \\ \text { Quantity } \\ \text { Supplied } \\ 1500 \text { Firms } \end{array} \\ \hline \$ 26 & \text {___} & \$ \text {_} & \text {_} \\ 32 & \text {_} & \text {_} & \text {_} \\ 38 & \text {_} & \text {_} & \text {_} \\ 41 & \text {_} & \text {_} & \text {_}\\ 46 & \text {_} & \text {_} & \text {_} \\ 56 & \text {_} & \text {_} & \text {_} \\ 66 & \text {_} & \text {_} & \text {___} \\ \hline \end{array}$$ e. Explain: "That segment of a competitive firm's marginalcost curve that lies above its average-variable-cost curve constitutes the short-run supply curve for the firm." Illustrate graphically. f. Now assume that there are 1500 identical firms in this competitive industry; that is, there are 1500 firms, each of which has the cost data shown in the table. Complete the industry supply schedule (column 4). g. Suppose the market demand data for the product are as follows: $$\begin{array}{|cc|} \hline \text { Price } & \begin{array}{c} \text { Total Quantity } \\ \text { Demanded } \end{array} \\ \hline \$ 26 & 17,000 \\ 32 & 15,000 \\ 38 & 13,500 \\ 41 & 12,000 \\ 46 & 10,500 \\ 56 & 9500 \\ 66 & 8000 \\ \hline \end{array}$$ What will be the equilibrium price? What will be the equilibrium output for the industry? For each firm? What will profit or loss be per unit? Per firm? Will this industry expand or contract in the long run?

Name: Problem 4, Chapter 9: Economics Principles, Problems, and Policies
Uploaded: 2021-01-19T20:34:39-08:00
Duration: 13 min 2 s
Channel: Lindsay Bur

   Assume the following cost data are for a purely competitive producer:
$$\begin{array}{ccccc}
\hline \begin{array}{c}
\text { Total } \\
\text { Product }
\end{array} & \begin{array}{c}
\text { Average } \\
\text { Fixed cost }
\end{array} & \begin{array}{c}
\text { Average } \\
\text { Variable cost }
\end{array} & \begin{array}{c}
\text { Average } \\
\text { Total cost }
\end{array} & \begin{array}{c}
\text { Marginal } \\
\text { cost }
\end{array} \\
\hline 0 \\
1 & \$ 60.00 & \$ 45.00 & \$ 105.00 & \$ 45 \\
2 & 30.00 & 42.50 & 72.50 & 40 \\
3 & 20.00 & 40.00 & 60.00 & 35 \\
4 & 15.00 & 37.50 & 52.50 & 30 \\
5 & 12.00 & 37.00 & 49.00 & 35 \\
6 & 10.00 & 37.50 & 47.50 & 40 \\
7 & 8.57 & 38.57 & 47.14 & 45 \\
8 & 7.50 & 40.63 & 48.13 & 55 \\
9 & 6.67 & 43.33 & 50.00 & 65 \\
10 & 6.00 & 46.50 & 52.50 & 75 \\
\hline
\end{array}$$
a. At a product price of $\$ 56,$ will this firm produce in the short run? Why or why not? If it is preferable to produce, what will be the profit-maximizing or loss-minimizing output? Explain. What economic profit or loss will the firm realize per unit of output?
b. Answer the relevant questions of 4 a assuming product price is $\$ 41$
c. Answer the relevant questions of 4 a assuming product price is $\$ 32$
d. In the table below, complete the short-run supply schedule for the firm (columns 1 and 2 ) and indicate the profit or loss incurred at each output (column 3).
$$\begin{array}{cccc} \hline
\begin{array}{c} 
\text { (1) } \\
\text { Price }
\end{array} & \begin{array}{c}
\text { (2) } \\
\text { Quantity } \\
\text { Supplied, } \\
\text { Single Firm }
\end{array} & \begin{array}{c}
\text { (3) } \\
\text { Profit }(+) \\
\text { or Loss }(-)
\end{array} & \begin{array}{c}
\text { (4) } \\
\text { Quantity } \\
\text { Supplied } \\
1500 \text { Firms } 
\end{array} \\
\hline \$ 26 & \text {_____} & \$ \text {_____} & \text {_____} \\
32 & \text {_____} & \text {_____} & \text {_____} \\
38 & \text {_____} & \text {_____} & \text {_____} \\
41 & \text {_____} & \text {_____} &  \text {_____}\\
46 & \text {_____} &  \text {_____} &  \text {_____} \\
56 &  \text {_____} &  \text {_____} &  \text {_____} \\
66 &  \text {_____} &  \text {_____} &  \text {_____} \\
\hline
\end{array}$$
e. Explain: "That segment of a competitive firm's marginalcost curve that lies above its average-variable-cost curve constitutes the short-run supply curve for the firm." Illustrate graphically.
f. Now assume that there are 1500 identical firms in this competitive industry; that is, there are 1500 firms, each of which has the cost data shown in the table. Complete the industry supply schedule (column 4).
g. Suppose the market demand data for the product are as follows:
$$\begin{array}{|cc|}
\hline \text { Price } & \begin{array}{c}
\text { Total Quantity } \\
\text { Demanded }
\end{array} \\
\hline \$ 26 & 17,000 \\
32 & 15,000 \\
38 & 13,500 \\
41 & 12,000 \\
46 & 10,500 \\
56 & 9500 \\
66 & 8000 \\ \hline
\end{array}$$
What will be the equilibrium price? What will be the equilibrium output for the industry? For each firm? What will profit or loss be per unit? Per firm? Will this industry expand or contract in the long run?

Economics Principles, Problems, and Policies

Campbell R.… 18th Edition

Chapter 9, Problem 4

Instant Answer

Solved by Expert Lindsay Bur

01/19/2021

Step 1

We know that a firm will produce in the short run as long as the price is above the minimum average variable cost (shutdown point). Looking at the table, we see that the minimum average variable cost is $37. Since $56 is greater than $37, the firm will produce in Show more…

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Assume the following cost data are for a purely competitive producer: $$\begin{array}{ccccc} \hline \begin{array}{c} \text { Total } \\ \text { Product } \end{array} & \begin{array}{c} \text { Average } \\ \text { Fixed cost } \end{array} & \begin{array}{c} \text { Average } \\ \text { Variable cost } \end{array} & \begin{array}{c} \text { Average } \\ \text { Total cost } \end{array} & \begin{array}{c} \text { Marginal } \\ \text { cost } \end{array} \\ \hline 0 \\ 1 & \$ 60.00 & \$ 45.00 & \$ 105.00 & \$ 45 \\ 2 & 30.00 & 42.50 & 72.50 & 40 \\ 3 & 20.00 & 40.00 & 60.00 & 35 \\ 4 & 15.00 & 37.50 & 52.50 & 30 \\ 5 & 12.00 & 37.00 & 49.00 & 35 \\ 6 & 10.00 & 37.50 & 47.50 & 40 \\ 7 & 8.57 & 38.57 & 47.14 & 45 \\ 8 & 7.50 & 40.63 & 48.13 & 55 \\ 9 & 6.67 & 43.33 & 50.00 & 65 \\ 10 & 6.00 & 46.50 & 52.50 & 75 \\ \hline \end{array}$$ a. At a product price of $\$ 56,$ will this firm produce in the short run? Why or why not? If it is preferable to produce, what will be the profit-maximizing or loss-minimizing output? Explain. What economic profit or loss will the firm realize per unit of output? b. Answer the relevant questions of 4 a assuming product price is $\$ 41$ c. Answer the relevant questions of 4 a assuming product price is $\$ 32$ d. In the table below, complete the short-run supply schedule for the firm (columns 1 and 2 ) and indicate the profit or loss incurred at each output (column 3). $$\begin{array}{cccc} \hline \begin{array}{c} \text { (1) } \\ \text { Price } \end{array} & \begin{array}{c} \text { (2) } \\ \text { Quantity } \\ \text { Supplied, } \\ \text { Single Firm } \end{array} & \begin{array}{c} \text { (3) } \\ \text { Profit }(+) \\ \text { or Loss }(-) \end{array} & \begin{array}{c} \text { (4) } \\ \text { Quantity } \\ \text { Supplied } \\ 1500 \text { Firms } \end{array} \\ \hline \$ 26 & \text {_____} & \$ \text {_____} & \text {_____} \\ 32 & \text {_____} & \text {_____} & \text {_____} \\ 38 & \text {_____} & \text {_____} & \text {_____} \\ 41 & \text {_____} & \text {_____} & \text {_____}\\ 46 & \text {_____} & \text {_____} & \text {_____} \\ 56 & \text {_____} & \text {_____} & \text {_____} \\ 66 & \text {_____} & \text {_____} & \text {_____} \\ \hline \end{array}$$ e. Explain: "That segment of a competitive firm's marginalcost curve that lies above its average-variable-cost curve constitutes the short-run supply curve for the firm." Illustrate graphically. f. Now assume that there are 1500 identical firms in this competitive industry; that is, there are 1500 firms, each of which has the cost data shown in the table. Complete the industry supply schedule (column 4). g. Suppose the market demand data for the product are as follows: $$\begin{array}{|cc|} \hline \text { Price } & \begin{array}{c} \text { Total Quantity } \\ \text { Demanded } \end{array} \\ \hline \$ 26 & 17,000 \\ 32 & 15,000 \\ 38 & 13,500 \\ 41 & 12,000 \\ 46 & 10,500 \\ 56 & 9500 \\ 66 & 8000 \\ \hline \end{array}$$ What will be the equilibrium price? What will be the equilibrium output for the industry? For each firm? What will profit or loss be per unit? Per firm? Will this industry expand or contract in the long run?

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Key Concepts

Marginal Cost (MC) Curve

The marginal cost curve represents the additional cost incurred when producing one more unit of output. It is crucial for decision-making since, in competitive markets, firms produce where price equals marginal cost. The MC curve also helps identify the optimal level of output at which profits are maximized and losses minimized, provided that the price covers the variable costs.

Average Costs (Fixed, Variable, and Total)

Average cost measures, including average fixed cost, average variable cost, and average total cost, provide insight into the cost per unit at various levels of production. The average fixed cost spreads the fixed cost over units produced, while average variable cost reflects the costs that change with output. Average total cost is the sum of these averages and represents the per-unit cost of production, which is essential in comparing with market prices to determine profitability.

Short-Run Supply Decision

In the short run, firms decide whether to produce or shut down based on the comparison of the market price to the average variable cost. If the price is above the minimum average variable cost, the firm will produce; if not, it will shut down even if fixed costs must be borne. The relevant portion of the marginal cost curve above the minimum average variable cost constitutes the firm's supply curve in the short run.

Profit Maximization in Competitive Markets

For firms operating in perfectly competitive markets, profit maximization occurs where the marginal cost equals the market price, as long as the price is not below the minimum average variable cost. This rule ensures that the firm produces the last unit that adds as much to revenue as it does to cost, thus optimizing output and profit or minimizing losses when equilibrium is not profitable.

Shutdown Rule

The shutdown rule governs a firm's decision to temporarily cease operations in the short run. It states that if the market price is below the minimum average variable cost, the firm should shut down production to minimize losses, as producing would incur additional variable costs that are not covered by the revenue. Fixed costs, being sunk in the short run, are not considered in this decision.

Industry Supply Curve

The industry supply curve is derived from the horizontal summation of all individual firms' supply curves. It represents the total quantity supplied at each price level in the market. Understanding the relationship between individual firm decisions and the aggregate industry supply is key to analyzing market equilibrium in competitive industries.

Market Equilibrium in Perfect Competition

Market equilibrium in a perfectly competitive industry is reached when the quantity supplied by all firms equals the quantity demanded by consumers at a particular price level. This equilibrium determines both the market price and the total industry output. It also implies that each firm produces at the optimal level where price equals marginal cost, ensuring no incentives for firms to change output in the short run.

Long-Run Adjustments

In the long run, the market is characterized by free entry and exit of firms. If firms are earning economic profits, new firms will enter, driving down the market price until only normal profits are made. Conversely, if firms incur losses, some will exit, pushing the price up until the remaining firms earn just enough to cover their opportunity costs. This process leads to a long-run equilibrium where firms operate at the minimum average total cost.

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Transcript

00:01 Today we are solving problem four from chapter 9 of economic principles, problems, and policies.

00:07 So this question gives us the values for average fixed costs, average variable cost, average total cost, and marginal cost for a firm, along with the total product at each point.

00:18 So what we want to find at the beginning of this question is that if the price in this market were $56, would the firm continue to produce? so we know that the zero profit point for a firm and the shutdown point for a firm between those two values is where a firm is going to produce.

00:37 So the zero profit point is where the average total cost is equal to the marginal cost or is also the minimum of the average total cost.

00:46 In this case, we can see that the minimum of the average total cost is $47 .14.

00:51 Cents.

00:52 Because a price of $56 is above the zero profit point, we know that this firm is going to produce at that price.

01:00 So the answer is yes.

01:03 So where would be the profit maximizing output at a price of $56? so in order to find the profit maximizing output, we are going to first find the total cost and total revenue in order to find the maximum profit.

01:16 So the total cost for this firm can be found by multiplying the average total cost by the total product.

01:25 So we need to multiply average total cost by the total product.

01:31 And this will give us the total cost at each unit.

01:35 Now we need to find the total revenue.

01:39 So we know that the total revenue at $56 is going to be equal to 56 times the total product.

01:48 Finally you want to find the profit at each unit.

01:50 So the profit would be the total revenue minus the total cost.

01:59 And as we can see, the profit maximizing output is going to be eight units because the profit is maximized at $62 .96 when we're producing eight units.

02:11 We would also like to find the profit per unit of output.

02:15 And in order to do this, we are going to divide the maximum profit by the output at that profit point.

02:22 So we know that the profit per unit of out point at eight units, units of output and a profit of $62 .96 is going to be $7 .87 per unit of output.

02:34 Now we're going to repeat this analysis with a price of $41.

02:38 So we know that the zero profit point is where the average total cost is at its minimum, which here we know is $47 .14.

02:49 Because $41 is below the zero profit point, we need to know if it's above the shutdown point in order to determine if the firm is going to produce.

02:58 So the shutdown point is going to be where the average variable cost is equal to the marginal cost or the minimum of the average variable cost.

03:05 And we can see that the average variable cost is at its minimum of $37.

03:11 And so a price of $41, we are going to see the firm produce because that price is above the shutdown point.

03:19 Like we did before, we want to know what the loss minimizing output would be.

03:25 Be at a price of $41.

03:27 So we already have the total revenue, so we're going to find, or the total cost, so we're going to find the total revenue.

03:33 At a price of $41, our total revenue is going to be 41 times the total product, and then we need to calculate our loss.

03:46 And we know it's going to be a loss because they are producing below the zero profit point.

03:50 So our loss is going to be our total revenue minus our total cost.

03:58 And we can see that the loss minimizing output is going to be at a loss of negative $39, which happens to be at a total product of six units.

04:07 We also want to find the loss per unit of output.

04:10 So as we did before, we are going to divide the loss minimizing point by the number of units of output at that point, which is negative $6 .50.

04:22 We are going to repeat our analysis for a final time at a price of $32.

04:27 So we know that a firm is going to shut down and stop producing at the shutdown point where the average variable cost is at its minimum or equal to the marginal cost.

04:36 We know that our average variable cost is at a minimum at $37.

04:40 Because the price is $32 and is less than the shutdown point, the firm is not going to produce at a price of $32.

04:49 Part d of this question would like us to fill in the short -run supply schedule at the price is given, for a single firm and for 1 ,500 firms.

04:58 So they are given us prices of 26 to 66 and it wants us to find what quantity would be the profit maximizing or loss minimizing quantity, what would be the profit or loss at that quantity, and what the quantity would be for 1 ,500 firms in the industry.

05:14 Up here i've copied over the total product and the total cost at that quantity that we calculated above.

05:20 What we want to do is calculate the profit at each price at each total product.

05:25 So first we're going to copy all of the prices from the cost schedule and transpose them over into this table.

05:39 Now that we have all the prices at the top, what we're going to do is find the profit at each price at each quantity.

05:46 So what we want to do is multiply the price times the quantity and that gives us our total revenue and subtract from that value the total cost.

06:00 So there we have the profit at $26 in price...

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