HOMEWORK #7
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?
P = MR, TC = AVC + AFC
AVC = TC/Q
Economic profit or loss = TR-TC
| 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, which is the highest, 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.
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?
If the firm sells its product for a price of $5, it would produce 4 units of output because, at that point, MC = $5 and P = MC.
If the firm sets the price to $7, the firm would produce 6 units of output because MC = 7 and P = MC.
If 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.
The firm sells its product 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.
When Price is 5 and Fixed Cost (FC) = 3
Total Cost = Variable Cost (VC) + Fixed Cost (FC)
Quantity = 4.
Profit = Price x Quantity – Total Cost
= 5(4) – (25+3)
= 20 – 28 = -8. The firm will have a negative profit.
When Price is 7, Quantity is 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:
Profit or loss = TR – TC
| 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?
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?
The firm should shut down in the short run because the firm is making losses since the firm incurs excess total cost and minimal total revenue.
- What is the relationship between MR and MC as the firm increases output?
MC is less than MR in the quantity 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 quantity of 3 to 7 units, an illustration that excess units are produced by the monopoly firm.
- 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
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
The profit maximizing Price of the monopoly is 8. The price of 8 coincides with quantity of = 10,000.
- total revenue
Total revenue = Price x Quantity = 8 x 10,000 = $ 80,000
- total cost
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
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