Perfect Competition Model
1.) Given the information below about Farmer Sally’s wheat crop, fill in the table below and calculate her economic profit or loss when the market price is $3 per bushel. Hint: Recall that MR = P under perfectly competitive conditions.
| Bushels of wheat | MR | TR | TC | MC | VC | ATC | AVC | Economic Profit or Loss |
| 0 | 3 | 0 | 15.00 | — | 0 | — | — | -15 |
| 1 | 3 | 3 | 19.75 | 4.75 | 4.75 | 19.75 | 4.75 | -16.75 |
| 2 | 3 | 6 | 23.5 | 3.75 | 8.5 | 11.75 | 4.25 | -17.5 |
| 3 | 3 | 9 | 26.5 | 3.00 | 11.5 | 8.83 | 3.83 | -17.5 |
| 4 | 3 | 12 | 29 | 2.50 | 14 | 7.25 | 3.5 | -17 |
| 5 | 3 | 15 | 31 | 2.00 | 16 | 6.2 | 3.2 | -16 |
| 6 | 3 | 18 | 32.5 | 1.50 | 17.5 | 5.4 | 2.92 | -14.5 |
| 7 | 3 | 21 | 33.75 | 1.25 | 18.75 | 4.8 | 2.68 | -12.75 |
| 8 | 3 | 24 | 35.25 | 1.50 | 20.25 | 4.4 | 2.53 | -11.25 |
| 9 | 3 | 27 | 37.25 | 2.00 | 22.25 | 4.1 | 2.47 | -10.25 |
| 10 | 3 | 30 | 40 | 2.75 | 25 | 4 | 2.5 | -10 |
| 11 | 3 | 33 | 43.25 | 3.25 | 28.25 | 3.9 | 2.57 | -10.25 |
| 12 | 3 | 36 | 48 | 4.75 | 33 | 4 | 2.75 | -12 |
| 13 | 3 | 39 | 54.5 | 6.50 | 39.5 | 4.19 | 3.04 | -15.5 |
| 14 | 3 | 42 | 64 | 9.50 | 49 | 4.57 | 3.5 | -22 |
| 15 | 3 | 45 | 77.5 | 13.50 | 62.5 | 5.17 | 4.17 | -32.5 |
| 16 | 3 | 48 | 96 | 18.50 | 81 | 6 | 5.06 | – 48 |
- Graph Total Cost and Graph Total Cost and Total Revenue on one graph and show the optimal point (either profit maximization or loss minimization).
- Graph MC, ATC, AVC, and MR on one graph and show the optimal point (either profit maximization or loss minimization). Shade in the area of profit or loss.
- If the price increased to $5 per bushel, what would be the economic profit or loss? How many bushels of wheat would Sally choose to produce?
Answer:
| Bushels of wheat | MR | TR | TC | MC | VC | ATC | AVC | Economic Profit or Loss |
| 0 | 5 | 0 | 15.00 | — | 0 | — | — | -15 |
| 1 | 5 | 5 | 19.75 | 4.75 | 4.75 | 19.75 | 4.75 | -14.75 |
| 2 | 5 | 10 | 23.5 | 3.75 | 8.5 | 11.75 | 4.25 | -13.5 |
| 3 | 5 | 15 | 26.5 | 3.00 | 11.5 | 8.83 | 3.83 | -11.5 |
| 4 | 5 | 20 | 29 | 2.50 | 14 | 7.25 | 3.5 | -9 |
| 5 | 5 | 25 | 31 | 2.00 | 16 | 6.2 | 3.2 | -16 |
| 6 | 5 | 30 | 32.5 | 1.50 | 17.5 | 5.4 | 2.92 | -2.5 |
| 7 | 5 | 35 | 33.75 | 1.25 | 18.75 | 4.8 | 2.68 | 1.25 |
| 8 | 5 | 40 | 35.25 | 1.50 | 20.25 | 4.4 | 2.53 | 4.75 |
| 9 | 5 | 45 | 37.25 | 2.00 | 22.25 | 4.1 | 2.47 | 7.75 |
| 10 | 5 | 50 | 40 | 2.75 | 25 | 4 | 2.5 | 10 |
| 11 | 5 | 55 | 43.25 | 3.25 | 28.25 | 3.9 | 2.57 | 11.75 |
| 12 | 5 | 60 | 48 | 4.75 | 33 | 4 | 2.75 | 12 |
| 13 | 5 | 65 | 54.5 | 6.50 | 39.5 | 4.19 | 3.04 | 10.5 |
| 14 | 5 | 70 | 64 | 9.50 | 49 | 4.57 | 3.5 | 6 |
| 15 | 5 | 75 | 77.5 | 13.50 | 62.5 | 5.17 | 4.17 | -25 |
| 16 | 5 | 80 | 96 | 18.50 | 81 | 6 | 5.06 | – 16 |
Sally should choose to produce 12 bushels of wheat because, at that quantity, a profit of 12 is made.
- What is Sally’s shutdown point? Answer this question in terms of both a minimum price that she would have to get in order to produce and a minimum quantity that she would be willing to make at the minimum price.
Answer:
Sally’s shut down point is at a minimum price of 3 and a minimum quantity of 1 because at that point, TR < AVC. For example, 3 < 4.75
- Consider a firm with the following short-run costs:
| Qty | TVC | MC | AVC |
| 1 | 10 | 10 | |
| 2 | 16 | 6 | 8 |
| 3 | 20 | 4 | 6.67 |
| 4 | 25 | 5 | 6.25 |
| 5 | 31 | 6 | 6.2 |
| 6 | 38 | 7 | 6.33 |
| 7 | 46 | 8 | 6.57 |
| 8 | 55 | 9 | 6.875 |
- Calculate the MC and AVC for each level of production (quantity).
- How much would the firm produce if it could sell its product for $5? For $7? for $10?
Answer: when the firm sells its product for $5, it will produce 4 units of output because, at that point, P= MC = $5.
When the Price = $7, the firm would produce 6 units of output because MC = 7 and P = MC.
When the Price is $10, the firm would produce 9 units of output because MC at that point is 10 and P = MC.
- Explain your answers.
Answer: The firm’s equilibrium is usually obtained at a point where MC = MR= Price.
- Assuming that its fixed cost is $3, calculate the firm’s profit at each of the production levels determined in part c.
Answers: When Price is 5 and Fixed Cost (FC) = 3
Total Cost = Variable Cost (VC) + Fixed Cost (FC)
Quantity = 4.
Profit = PQ – TC
= 5(4) – (25+3)
= 20 – 28 = -8. The firm will have a negative profit.
When Price is 7, Q is equal to 6
Profit = PQ – TC
= 7(6) – (38+3)
= 42 – 41 = 1. The profit will be 1
When Price is 10, Quantity is 9
Profit = PQ – TC
= 10(9) – (65+3)
= 90 – 68 = 12. The profit will be 12.
- A monopoly firm has the following demand and cost structure in the short run:
| Q | P | TFC | TVC | TC | MC | TR | MR | Profit/Loss |
| 0 | 100 | 100 | 0 | 100 | 0 | -100 | ||
| 1 | 90 | 100 | 50 | 150 | 50 | 90 | 90 | -60 |
| 2 | 80 | 100 | 90 | 190 | 40 | 160 | 70 | -30 |
| 3 | 70 | 100 | 150 | 250 | 60 | 210 | 50 | -40 |
| 4 | 60 | 100 | 230 | 330 | 80 | 240 | 30 | -90 |
| 5 | 50 | 100 | 330 | 430 | 100 | 250 | 10 | -180 |
| 6 | 40 | 100 | 450 | 550 | 120 | 240 | -10 | -310 |
| 7 | 30 | 100 | 590 | 690 | 140 | 210 | -30 | -480 |
- Complete the table.
- What is the best profit or loss available to this firm?
Answer:
The best loss available to the firm is 30; at that point, the total cost is 190, while the total revenue is 160. losses are minimal at that point.
- Should the firm operate or shut down in the short run? Why?
Answer:
The firm should shut down in the short run because the firm is making losses since the firm incurs high total cost and low total revenue.
- What is the relationship between MR and MC as the firm increases output?
MC is less than MR in the output of 1 and 2 units, which means that the company is not producing sufficient units. On the other hand, MC is higher than MR from the output of 3 to 7 units, an illustration that excess units are produced by the monopoly.
- The following diagram shows the cost structure of a monopoly firm as well as market demand. Identify on the graph and calculate the following:
- profit-maximizing output level
Answer:
The profit-maximizing output level of a monopoly occurs at appoint where MR = MC. From the diagram, the point where MR = MC coincides with a quantity of 10,000.
- profit-maximizing price
Answer:
The profit maximizing Price of the monopoly is 8. The price of 8 coincides with quantity of = 10,000.
- total revenue
Answer:
Total revenue = Price x Quantity = 8 x 10,000 = $ 80,000
- total cost
Answer:
The output of 10 000 coincides with ATC at a price of $ 9.
TC = Q x ATC = 9 x 10,000 = $ 90 000
- total profit or loss
Answer:
Total loss since the Price is less than ATC.
Total loss = TC – TR = $90 000 – $80 000= $10 000
$
MC ATC
9
8
3
D
10,000 Qty
MR