A shoe manufacturer notices the following relationship between the number of workers employed and quantity of shoes produced in a day.
Q. (VC). (TC). (MC).
quantity . variable cost total cost marginal cost. AVC. ATC
0 0 90 - - -
1 9 99 9 9.0 99.0
2 24 114. 15 12.0 57.0
3 54 144 30 18.0 48.0
4 102 192 48 25.5 48.0
5 162 252 60 42.0 68.0
6 252 342 90 42.0 57.0
7 360 450 108 51.4 64.3
8 480 570 120 60.0 71.3
9 630 720 150 70.0 80.0
A). what is the companies efficient scale?
B). suppose the industry price is 108$. what is the company qmax? calculate its profit or loss and producer surplus. is the firm in short run or long run equilibrium?
C). suppose the industry price is 48$. what is the company's qmax?calculate its profit or loss and producer surplus. is the firm in short run or long run equilibrium?
D). suppose now the price falls to 15$. what are the company's qmax and profit or loss? what is the producer surplus? is the firm in short run or long run equilibrium?what should the company production decision be?
A) The company's efficient scale is the level of output at which average total cost is minimized. Looking at the ATC column, we can see that the lowest point is at a quantity of 6, where ATC is $57. Therefore, the company's efficient scale is 6.
B) At a price of $108, the company's qmax is the quantity at which MC = P. From the MC column, we can see that this occurs at a quantity of 7. Therefore, the company will produce and sell 7 pairs of shoes.
To calculate the profit or loss, we need to find the company's total revenue and total cost at a quantity of 7. Total revenue can be found by multiplying the price by the quantity, which gives us $756. Total cost can be found in the TC column, and at a quantity of 7, it is $450. Therefore, the company's profit is $306.
To calculate producer surplus, we need to find the area above the supply curve and below the price at a quantity of 7. This is represented by the shaded triangle in the graph below. To find the area, we can use the formula (1/2) x base x height. The base is 7 (the quantity), and the height is the difference between the price and the variable cost at a quantity of 7, which is $99. Therefore, the producer surplus is (1/2) x 7 x $99 = $346.50.
Graph:
```
P = $108
/ |
/ |
/ | Producer surplus
/ | /
/ | / Profit
/ | /
/ | /
--------|-----------------
|/
Q = 7
```
Since the company is making a profit, it is in short run equilibrium. To determine if it is in long run equilibrium, we need to see if it is operating at its efficient scale. From part A), we know that the company's efficient scale is 6, but it is producing at a quantity of 7. Therefore, the company is not in long run equilibrium.
C) At a price of $48, the company's qmax is the quantity at which MC = P. From the MC column, we can see that this occurs at a quantity of 4. Therefore, the company will produce and sell 4 pairs of shoes.
To calculate the profit or loss, we follow the same steps as in part B). Total revenue is $192 (4 x $48), and total cost is $192 (from the TC column at a quantity of 4). Therefore, the company breaks even and makes no profit or loss.
To calculate producer surplus, we follow the same steps as in part B). The shaded triangle in the graph below represents the producer surplus. The base is 4, and the height is $45 (the difference between the price and variable cost at a quantity of 4). Therefore, the producer surplus is (1/2) x 4 x $45 = $90.
Graph:
```
P = $48
/ |
/ |
/ | Producer surplus
/ | /
/ | /
/ | /
/ | /
--------|-----------------
|/
Q = 4
```
Since the company is breaking even, it is in short run equilibrium. To determine if it is in long run equilibrium, we need to see if it is operating at its efficient scale. From part A), we know that the company's efficient scale is 6, but it is producing at a quantity of 4. Therefore, the company is not in long run equilibrium.
D) At a price of $15, the company's qmax is the quantity at which MC = P. From the MC column, we can see that this never occurs, so the company will shut down and produce zero pairs of shoes.
To calculate the profit or loss, we need to find the company's total revenue and total cost at a quantity of 0. Total revenue is 0, since the company is not producing any shoes. Total cost is the fixed cost, which in this case is $90 (from the TC column at a quantity of 0). Therefore, the company's loss is $90.
To calculate producer surplus, we can see from the graph below that there is no producer surplus at a price of $15 and a quantity of 0.
Graph:
```
P = $15
/
/
/
/
/
/
/
/
-------------------------Q = 0
```
Since the company is making a loss, it is not in short run or long run equilibrium. The company should shut down and not produce any shoes, since it would lose $90 by doing so.
I don't understand how the producer surplus is calculated? graphs are not visible
I apologize for the confusion. Let me explain how to calculate producer surplus without the graph:
Producer surplus is the difference between the price and the variable cost per unit, multiplied by the quantity produced.
For example, at a price of $108 and a quantity of 7, the variable cost per unit is $51.4 (VC column divided by the quantity). So the producer surplus per unit is $108 - $51.4 = $56.6.
To find the total producer surplus, we multiply this by the quantity produced, which is 7. So the total producer surplus is $56.6 x 7 = $396.2.
Similarly, at a price of $48 and a quantity of 4, the variable cost per unit is $25.5 (VC column divided by the quantity). So the producer surplus per unit is $48 - $25.5 = $22.5. To find the total producer surplus, we multiply this by the quantity produced, which is 4. So the total producer surplus is $22.5 x 4 = $90.
I hope this helps!
A) The company's efficient scale can be determined by looking at the quantity of output where the average total cost (ATC) is at its minimum. In this case, looking at the ATC column, we can see that the minimum ATC occurs when the quantity is 6, with an ATC of 57.0. Therefore, the efficient scale for this company is a quantity of 6.
B) To find the company's qmax (quantity at which it maximizes profit), we need to look at the marginal cost (MC) and the average variable cost (AVC) columns and identify the quantity at which MC intersects AVC. In this case, when the industry price is $108, the qmax is 7, as the MC ($108) intersects the AVC ($51.4) at this quantity.
To calculate the profit or loss, we need to subtract the total cost (TC) from the total revenue (TR). The total revenue can be calculated by multiplying the industry price by the quantity. In this case, the total revenue is $108 multiplied by 7, which equals $756. The total cost at this quantity is $450.
Profit or loss = Total Revenue - Total Cost
Profit or loss = $756 - $450
Profit or loss = $306
To calculate the producer surplus, we need to find the area between the industry price and the supply curve (which is the marginal cost curve). In this case, the area between the industry price ($108) and the marginal cost curve is a triangle with a base of 7 (quantity) and a height of $57. The formula for calculating the area of a triangle is (1/2) x base x height.
Producer surplus = (1/2) x base x height
Producer surplus = (1/2) x 7 x $57
Producer surplus = $199.5
This firm is in short-run equilibrium because it is maximizing profit where MC intersects AVC. However, we don't have enough information to determine if it is in long-run equilibrium. We would need to know the industry demand and the average total cost at different quantities to determine if the firm is earning zero economic profit in the long-run equilibrium.
C) When the industry price is $48, we can find the qmax by identifying the quantity at which MC intersects the industry price. In this case, the qmax is 4. The profit or loss can be calculated in the same way as mentioned earlier:
Profit or loss = Total Revenue - Total Cost
Total Revenue = $48 x 4 = $192
Total Cost = $192
Profit or loss = $192 - $192
Profit or loss = $0
The producer surplus, in this case, is also zero since the industry price is equal to the average variable cost.
This firm is also in short-run equilibrium because it is still maximizing profit where MC intersects AVC. Again, the information provided is not enough to determine if it is in long-run equilibrium.
D) When the price falls to $15, we can find the qmax by identifying the quantity at which MC intersects the industry price. In this case, the qmax is 0, as the MC is higher than the price at all quantities and the firm would not produce any output.
The profit or loss can be calculated as:
Profit or loss = Total Revenue - Total Cost
Total Revenue = $15 x 0 = $0
Total Cost = $90
Profit or loss = $0 - $90
Profit or loss = -$90
The producer surplus is also zero since there is no output produced.
In this case, the firm is not in short run or long-run equilibrium because it is not producing any output. The firm should consider shutting down production in the short run as it is incurring a loss and the price is lower than the variable cost. In the long run, the firm may have to exit the market if it continues to face losses.