The 6th unit fencing costs $11.67 on average.
The Diminishing returns begin at the 6th unit of output.
Terminus earns $8 profit at its production of 4 units.
Terminus operates in the short run due to positive profit.
Terminus won't stay in the long run due to zero profit in perfect competition.
How is that so?
Finding the average total cost of the 6th unit of fencing:
The average total cost (ATC) is calculated by dividing the total variable cost (TVC) by the quantity (Q). For the 6th unit of fencing, the ATC is:
ATC = TVC(6) / Q(6)
From the table, we can find that TVC(6) = $70.
Therefore, the ATC for the 6th unit is:
ATC = $70 / 6 units = $11.67 per unit
Finding the first unit of output where diminishing marginal returns have begun:
Diminishing marginal returns occur when the marginal product (MP) starts to decrease. The MP is the change in total output (Q) caused by a one-unit increase in the input (variable factor). In this case, the input is the number of units of fencing produced.
We can calculate the MP for each unit of fencing using the formula:
MP = ΔQ / Δunits
From the table, we can calculate the MPs as follows:
MP(1) = (1 unit - 0 units) / (1 unit - 0 units) = 1 unit/unit
MP(2) = (2 units - 1 unit) / (2 units - 1 unit) = 1 unit/unit
MP(3) = (3 units - 2 units) / (3 units - 2 units) = 1 unit/unit
MP(4) = (4 units - 3 units) / (4 units - 3 units) = 1 unit/unit
MP(5) = (5 units - 4 units) / (5 units - 4 units) = 1 unit/unit
MP(6) = (6 units - 5 units) / (6 units - 5 units) = 0.8 unit/unit
As you can see, the MP starts to decrease at the 6th unit (MP(6) < MP(5)). Therefore, diminishing marginal returns begin at the 6th unit of output.
Calculating economic profit or loss at the profit maximum:
The profit is maximized when the marginal cost (MC) equals the marginal revenue (MR). In a perfectly competitive market, the MR is equal to the price of the good. Therefore, the profit-maximizing quantity (Q*) can be found by setting MC = P:
MC = P = $12 per unit
From the table, we can see that MC = $12 per unit at Q = 4 units. Therefore, the profit-maximizing quantity is Q* = 4 units.
To calculate the economic profit at Q*, we can use the formula:
π = (P - ATC) * Q*
From the table and previous calculations, we know that ATC(4) = $10 per unit. Therefore, the economic profit at Q* is:
π = ($12 - $10) * 4 units = $8
Therefore, Terminus would earn an economic profit of $8 at its profit maximum.
Operating in the short run:
Whether or not Terminus operates in the short run depends on whether its price is above its average variable cost (AVC). If the price is above the AVC, then Terminus will cover its variable costs and make a positive economic profit. Otherwise, it will incur a loss and may choose to shut down in the short run.
From the table, we can see that the AVC is $8 per unit. Since the price is $12 per unit, which is above the AVC, Terminus will cover its variable costs and make a positive economic profit in the short run. Therefore, it will choose to operate.
Staying in the market in the long run:
In the end, firms in a perfectly free competition will earn nothing economic profit. This is cause, in the long run, there is free access and exit. If any firm is making an business-related profit, new firms will enter stock exchange and drive down the price as far as the profit is zero. Likewise, if any firm is making a misfortune, it will exit the market.
Thus, in the long run, End will not be able to maintain allure economic profit of $8. The price will ultimately fall to $10 apiece, which is prepared the minimum average total cost (minimum ATC).