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Suppose that a perfectly competitive firm has the following total variable costs $(T V C):$Quantity: $\quad 0 \quad 1 \quad 2 \quad 3 \quad 4 \quad 5 \quad 6$TVC: $\quad \$ 0 \quad \$ 6 \quad \$ 11 \quad \$ 15 \quad \$ 18 \quad \$ 22 \quad \$ 28$It also has total fixed costs $(T F C)$ of $\$ 6 .$ If the market price is $\$ 5$ per unit:a. Find the firm's profit-maximizing quantity using the marginal revenue and marginal cost approach.b. Check your results by re-solving the problem using the total revenue and total cost approach. Is the firm earning a positive profit, suffering a loss, or breaking even?
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hello. In this video, we're going to look at a perfectly competitive firm on. We know that we have. We know the total revenue because of off this form and their corresponding quantity. And we also know that the fist costs off this firm. It's $6 and we know that the price, which is also the marginal revenue did that this firm could make on this market would be $5. And we want to know what is the profit maximizing or lost minimizing comedy that a firm should produce. And there are two approaches to softest kind of problem. The first approach is to first figure out the marginal costs. Given the diagram given this table, um, for this company and we look for the point where marginal cost he's actually small or you kowtow Mark are to the price or marginal revenue price or marginal revenue and and we will keep producing until the marginal costs become great heard in the price. Um, and this is our first approach, So let's start from there. So, given the total revenue, Toto told a variable cost, we could figure out a marginal cost. So from zero unit to one unit. The variable cost occur is six daughters, so the marginal cost will be $6. Um, from one unit to two units, total revenue total very because become $11. And the difference between first unit on the second unit, second unit and the first you know, is five daughters. So the marginal cost is five. So to save space, I'm going to just keep a five here from two units to three units, the additional costs is 15 minus 11 which is $4 from three units to four units. Additional cost is 80 minus 15 which is three dollars, and from 54 units to five units. The additional cost is 20 to minus 18 which is $4 from 5 to 6. Costs increase by again $6. So we can see that at the very beginning, marginal cost is greater than the marginal revenue wishes. $5. But if we increase our production to two units, we see the marginal cost because to marginal to the price wishes to marginal revenue and you keep increasing our production from 2 to 3, the motion of costs is lower. Then the price. So wish we are actually making it making some marginal profits if we increase our production from tune in two units to three units. And if we keep going, the marginal Kostas even lower. So we're actually making additional war additional profits by increasing production from 3 to 4. Right? And if we keep producing for Eunice to five units, we see that the marginal cost is $4 any school lowered and the marginal price again. So we had making additional profits if we increase our production. However, if we increase from 5 to 6, we know the emotional cost is greater than the marginal revenue here. So making this additional production, our total revenue were actually increased because this additional units we produce which and the rate of loss. So for this firm, you should keep producing onto they reach five units and stopped producing at this point, right, Because producing additional unit here we generate loss. So our answer is the firm show actually produced five units and we have an additional question that we need to answer, which is whether or not at this five units, the firm is making profits or generating loss. To answer this question, which it might be easier if you look at our second approach to solve this question, Our second approach is using the total car, total revenue and total cost function. So we want to know we know that the profits that the firm produce or generates it's the difference between the total revenue and the total cost. Right? So we could, given the costs off this firm we know is total revenue at all available cars. Until the office costs, we could calculate the total total cost for just from a different units, and we know the price off the product. So we know the total revenue that this firm could generate so we could figure out its creed, the profits at different units that the firm can generate. And we can then decide what is the profit maximizing or loss of minimizing, Ah, quantity that affirms going to produce. So So, to do this, we less just figure out what is the total cost for this firm at different units. So remember that total cost is the sun off total variable costs and told her office cost or the fiscus Okay, so that's just easy calculation, right? So at zero units, the firm. It's not generate, not generate rating any in verbal Cosper ease. Pain is Fisk Cost. So is $6 total Cost us $6 at one units. Total cost is six plus six, which is Trav A two units. We have 17 at three units. We have 21 and four units. We have 18 plus six, which is 24 of five units. We have 22 plus six, which is 28 as six units. We have 28 plus six, which is 34. Okay, Okay. So just to save space, I'm going to the races. This we have the total cost already, and we also need to figure out the total revenue. Right? Total revenue is basically price times quantity. We know price is $5 so we just need to get a multiply the quantity by five to calculate the total revenue at different units. So it's zero total revenue will be zero right At one unit, it'll room there will be five a two units we have five times to, which is 10. If four units is £5.3 which is 15 and then we keep going at four. Is five pence. ah fi. Five pence four is 20. Then five times 55 times six, which is 30. So then we can calculate the profits. Profit is just the difference between total revenue and total cost. Right at 040 net swimming were generating loss off $6 at one units. Total causes craft. Total revenue is five. Then we're losing $7. Same for two units still lost. Still losing $7 at three units were losing alot. Bulus, which is $6 a four units were losing again, $6 at five units. Rial losing 28 to minus trend A 25 minus 28 which is never 50. And the six units were losing $4. So as we can see, right the firm, it's always making generating loss. Oh, at In these markets, however, the loss is smallest again at a unit off five. So we had get to the same answers using the two different approaches. Right, So their first approach is we figure out a marginal cost and find a marginal costs, and we we want the marginal cost to be lower than the price. Um and we found the corresponding quantity and Our second approach is a little bit more complicated. We write out right down all the total cost of different units red on the total revenue at this units and then calculate the profits at different units. And we find the units so that the profits the smallest or are the loss of Smalls or the profits largest?
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