hi everyone in this video I'm going to discuss profit maximization in perfect competition so I'll just start with thinking about our firm's profit function so profit Pi is equal to total revenue that's TR that's all of the revenue that the firm gets from Trading minus the total cost of production TC in order to maximize this profit function I'm just going to take the derivative of the function with respect to quantity q and then I'll set that derivative equal to zero and this will tell us about the conditions that the firm needs to fulfill if they want to profit maximize so just on the right hand side of this screen here then let's take the derivative of our profit with respect to quantity and that's just going to be equal to the derivative of each of its component parts with respect to quantity so we'll have the derivative of total revenue with respect to quantity minus the derivative of total cost with respect to quantity our derivative of our total revenue with respect to quantity is just our marginal revenue so that's Mr and our derivative of our total cost function with respect to quantity is just marginal cost MC and we're going to set all of that equal to zero in order to maximize our profit just thinking about that last equality if we add marginal cost to MC to both sides we get this condition that if the firm wants to maximize profit they're going to set their quantity such that marginal revenue is equal to marginal cost so that's the general condition of profit maximization for our perfectly competitive firm however when they produce and sell an additional unit the additional Revenue that they get from that increase in production that's their marginal revenue is always just equal to the price and that's because the firm in perfect competition is a price taker they take the price that's determined in the market is given so marginal revenue is equal to the price for the perfectly competitive firm and this all means that when we think about profit maximizing condition you know setting quantity such that marginal revenue is equal to marginal cost well for the perfectly competitive firm this is actually extended out to the price is equal to marginal revenue is equal to marginal cost and from this kind of set of equalities let's just put aside the marginal revenue term in the middle and we see that the profit maximizing condition for the perfectly competitive firm requires the firm to set their quantity such that price is equal to Marginal costs so I do like thinking about the profit maximization decision for the perfectly competitive firm in this way set price equal to marginal cost because it just shows really clearly that in perfect competition the price that the consumer pays is equal to the cost of production which is actually one of the characteristics of perfect competition that there is no markup over price if we look to our diagrams all of this looks like the following we have a market diagram on the left hand side so we have our market demand which is the sum of our consumers demand curves and our market supply curve which is the sum of our Producers Supply curves the price in the market is determined at the intersection of these two curves so that will give us P star and it will also give us big Q star that's the quantity that is traded in the market now our perfectly competitive firm being a price taker is just going to take that market prices given so on the right hand side diagram here I have a marginal cost curve for a representative firm in the market so there are many many firms in perfect competition this is the marginal cost curve for just one and profit maximization for that firm will look like this the firm takes that price P star which is also their marginal revenue and sets that equal to marginal cost and that will give us our small q star that's our firm's optimal level of production that's going to maximize profit now it is worth thinking about this a little bit with our diagrams from our diagrams how can we see that Q star is the optimum well we can ask ourselves what if for instance we produced q1 Which is less than Q star well you can see that for q1 the marginal revenue that's just the price line is higher than the marginal cost and that's really good it's good to produce when our revenue is higher than costs but then you can see that the marginal revenue for all of these other units to the right of q1 that we haven't produced well their revenue is greater than the marginal cost of production too and we should produce these units because the revenue that we get will be higher than the cost that would give us more profit so q1 is not maximizing profit because we wouldn't be producing enough The Firm would miss out on a heap of units of production where the marginal revenue was greater than the marginal cost and we can actually use this argument for any quantity less than Q star if we produce where the quantity is less than Q star we're just not exhausting all of the possible levels of production where our marginal revenue is higher than marginal cost so that wouldn't be an Optimum we can make a similar argument for any quantity above Q star and so I'm just going to extend out the price line let's take Q2 here and just drawing up you can see that the marginal cost of production so how much it costs to make that unit is greater than the marginal revenue that the firm would get if it sold that unit so marginal cost is higher than the price and of course it's a bad idea to produce this unit we shouldn't produce if the costs are higher than the revenue that we're we're getting so Q2 is definitely not maximizing profit we should not make Q2 we can make that argument for any quantity above Q star so for all of these units above Q star the marginal cost is above the marginal revenue so we really shouldn't be producing those units so our optimal can't be any quantity smaller than Q star and it also can't be any quantity larger than Q star so it really just has to be Q star that's our profit maximization choice for the firm now there are two caveats to this the first one is that in the short run the price does have to be greater than or equal to our average variable costs and that's AVC or else The Firm will shut down they will produce zero the second caveat is that in the long run the price has to be greater than or equal to average total cost that's ATC or the firm will leave the industry they won't produce a positive amount so we set price equal to marginal cost in order to profit maximize but we do have to check that these conditions are satisfied so I'll stop the video here just because I don't want to draw it out too much but there is heaps more to say on this topic I do have another video for instance where I explain these caveats that I just described and in that video I go through the diagrams more thoroughly I also have an Associated practice problem so I'll link to that as well in any case I hope that this all helped and hope you guys are doing well and keeping happy and safe