 So, we will continue our discussion on non-collisive oligopoly model also in this session. So, if you remember in the last class, we discussed about the connoit models and connoit models typically a duopoly market situation, where the basic characteristic is that it operates in zero cost of production and that is why we get a marginal cost which is equal to zero and here even if the firm they knows that they are interdependent on each other, but when they fix their output, when they fix their price, they are not taking into consideration the what will be the rivals plan on the basis of their revised plan and that is the reason if you remember in the last class, we discussed a situation when in the period they one fourth of the market remain unexplored, no one produce in that one fourth market, the rest three fourth market is got produced by both the firms A and B. So, we will continue our discussion on the connoit model, we will see that how the equilibrium solution can be achieved or how the equilibrium can be achieved with the reaction and action patterns of the reaction and action pattern of the two firms. So, in the last class, if you remember we talked about a situation where the three fourth of the market generally so, in that case if you remember then A B together they were just producing three fourth of the market and one fourth was not produce either by firm A or firm B at least in the first period. Now, what will happen in period two? So, this in the first case three fourth was produced together by A and B and one fourth was not. Now, how it will happen in period two? From A assume that B just going to produce one fourth of it and he will feel that three fourth is his own market typically for firm A. So, if three fourth is his own market now generally he producing only half of it. So, he will produce half of three fourth in the market and that will come to three eighth of total market. So, A is going to produce three eighth of total market. A assume that B just going to produce one fourth of the market. So, A will think that he is just going to produce only three fourth or the rest three fourth is his own market and he is since A produce only half of the total market in this case the half of total market is half multiplied by three fourth and that comes to three by eight as the total market. Now, we will see how B is going to react to this. So, B will consider that again when it comes to B what will be the assumption for B? The assumption for B is A will continue to produce three eighth of the market means what is the market available for B? The remaining market that is less by three by eight. So, this is one by three eight is the market available to B. Now, B will produce again half of this because half of one by one minus three by eight. So, this is five by sixteen. So, A is going to produce three by eight and B is going to produce five by sixteen. Now, this action reaction pattern continues from always assume that A always assume that B is going to produce half and from B is always going to assume that A is going to produce half. So, they take out that half and they feel that the rest of the market whatever they could produce and again it comes the half of the total market demand. So, this action reaction pattern for form A and B will continue. Now, what is the outcome of this action reaction pattern of form A and B? So, it just goes on with the share that is half of share half of the total market except the share of A for B and half of the total market except the share of B for A. So, this action reaction will continue. So, in this action reaction generally share of A goes on decreasing and share of B goes on increasing and this will lead to a situation where each form supplies to an equal market that is one third of the total market. So, this if you look at initially the share of A was higher than share of B. So, this action reaction pattern will continue and with the action reaction pattern finally, each form will reach to a situation where they are just producing one third of the total market and remaining this one third of total market is produced by A, one third of total market is produced by B and remaining one third is not getting produced either by A or by B. So, we will just take the graph to understand this that how this reach to a situation where they just produce one third, one third and leads to a case where rest one third is remain on produce either by A and B. So, if you remember your reaction function R 1, R 1 dash is the reaction function of form A, R 2, R 2 dash is the reaction function of form B. So, ideally this should be the situation where this is the amount of Q 1, this is the amount of Q 2, Q 1 is produced by A, Q 2 is produced by B. Now, how they reach to this Q 1, A to Q 1, B? It is not they start from here, rather they start from here and what is this R 1 dash here? At this point the total market demand is we can say O R 2 dash is the total market demand. So, out of this initially A will just produce this much and from there actually this action reaction pattern happens. So, if this A is producing this corresponding to this B will produce here that in the reaction curve of B. R 2, R 2 dash is the reaction curve function of B, R 1, R 1 is the reaction curve function of A. So, if you look at if initially A produce this much, now with reaction to this B will produce take a point corresponding to this in the reaction function of B that is R 2, R 2 dash corresponding to this again A will react to this and choose a combination where in the reaction function of A and if you remember what is reaction function? Reaction function gives the different quantity of Q 1 and Q 2, combination of Q 1 and Q 2 where profit is maximum. So, whether B chooses any combination in reaction function 2, A chooses any combination in reaction function 1 ideally they maximize the profit. So, to start with they will do this with A start with this point corresponding to this B choose a combination over here. Now, suppose this is combination 1 then this is combination 2 again chosen by A with respect to the reaction to a combination B by this 1. Then corresponding to this again B will choose a combination here and corresponding to this A will choose a combination here, then corresponding to this again B will choose a combination here and here A will choose a combination here. The action reaction will continue till the time they are not reaching this point E and after reaching the point E, they generally they reach the equilibrium solution where A produce Q 1 unit of output and P produce Q 2 unit of output. So, graphically how we reach the Carnot equilibrium? We reach the Carnot equilibrium through the reaction function approach. We take the reaction function 1, reaction function 2 and the reaction of both the forms get captured in their own reaction function. And finally, eventually this reaction action pattern leads time to the equilibrium, where they this is generally stable and after that at least in that time period again the reaction action pattern never continue. Then we will see the detailed description that how this one-third of this total total market output comes to form 1, we will just take period wise that how this final yield comes to one-third for form A and one-third for form B. So, if you generally we will just take a form of equation in order to understand this. So, period 1 we will see what is form A, what is form B. So, form A is half of total market. So, this is half, form B is half of half market that is a share that comes to one-fourth. Then period 2 what will be for form A, half of 1 minus 1 4, 1 4 is the B share that comes to 3 by 8. Then what will be for form B that is half of 1 minus 3 by 8 that comes to 5 by 16. Now, what will be in period 3 form A that is half of 1 minus 5 by 16, this is B share that comes to 11 by 32. So, this is B share 1 minus this half of it going to be produced by form A, form B again half of 1 minus 11 by 32 this is share of A. So, this comes to 21 by 6 4. Then we will talk about period 4 output of form A and form B. So, this is nothing but just taking the share and making a half of it, but eventually we will see how they just produce one-third of the total output. So, for period 4 this is again half of 1 minus 11 by 32. So, that comes to sorry 1 minus 21 by 64. So, that comes to 43 divided by 128 and form B again half by 1 minus 43 by 128. So, that comes to 85 by 256. Now, this continue till the time period n. So, we will see how what will be the value in period n, because n takes any number. So, it is 1 to n. So, in period n what will be the share of form A and form B. Eventually it is form A half by 1 minus 1 by 3. So, that comes to 1 by 3 and form B half of 1 by 1 minus 3 that is coming to 1 by 3. Now, what is A's equilibrium output now? A's equilibrium output will be half minus 1 by 8 by 1 by 1 minus 4. So, that comes to half minus 1 by 8 by 3 by 4 which comes to 8 by 24 and 1 by 3. This is form A, forms A equilibrium output. Similarly, we will find form B's equilibrium output. So, form B's equilibrium output 1 4 by 1 minus 1 4. So, this is 1 by 4 divided by 3 by 4 which comes to 1 by 3. And for n number of form what will be the industry output and what will be the firms output? Industry output will be n by n plus 1 or to again describe this. This is E is equal to 1 summation E 1 to n 1 by n plus 1. And what will be the individual firms output? n 1 by n plus 1. This will be the individual firms output both for A and B. So, ideally what we want to check over here? We want to check over here is that when the action reaction pattern happens they assume the same behavior from other firms. And that is why if you find some of this which remain on utilize that is not being produced either by firm A or firm B. And that is why they are just producing one-third of the total output of the market and remaining one-third is not being produced either by A and B. Next we will see we will just take an example to understand this Conert model. We will just take a numerical to understand the Conert's model and then we will move into the next model that is Stackelberg model and Paul Swiggy King demand Curve model. So, P is equal to 100 minus 0.5 x. This is the demand function. This is cost function of firm A which is it is a constant cost function. For firm B it is the increasing cost function. We need to find out the profit maximizing level of output for both the firm A and B. And how we will find out this? We generally take the profit maximizing rule that is marginal revenue is equal to marginal cost. So, what is this P? P we can simplify this as 100 minus 0.5 x A plus x B because this x is the total output is the summation of output of A and B. And what will be the profit of A? What will the profit of firm A? That is total revenue minus total cost. And what is total revenue over here? So, total revenue minus total cost will give us the profit of A. So, this is P x A. This is the output. This is the price minus 5 x A. This is the cost function of the firm A. So, what is P x A? That is 100 minus 0.5 that is x. So, this is x A plus x B multiplied by x A minus 5 x A. So, this is cost function. This is P and this is x A. So, if you simplify this then it comes to 100 x A minus 0.5 x A square plus sorry, if you open the bracket this is minus 0.5 x A x B minus 5 x A. Simplifying this again, this is 95 x A because this 5 x A will get deducted from here minus 0.5 x A square minus 0.5 x A and x B. Simplifying this 95 minus x A minus 0.5 x B is equal to 0. So, this is our marginal that is our this profit. So, this comes to marginal revenue equal to minus marginal cost has to be equal to 0. So, this is 95. If you take the derivative then this comes to 95, this comes to x A, this comes to 0.5 x B. So, if you simplify this in term of x A, this comes as a 95 minus 0.5 x B and what is this x A in term of x B? This is the reaction function of A, this is the reaction function of A. Similarly, we will find the reaction function of B and if you remember what is the reaction function of A, this combination gives the maximum level of profit to the firm A. Similarly, we will now find it for B. So, if you simplify this for x B, we get its 50 minus 0.25 x A. So, I am not just doing a detailed calculation for B, you need to follow the same formula to find out the what we did for A, the same formula to find out the reaction curve function for B. Basically, you need to find out the pi, then you have to maximize it, pi is the difference between total revenue, total cost, you need to maximize this and then solve for the value in term of x B in term of x A and that will give us the reaction curve function for reaction curve function for B. Now, to find this value of x A and x B, we need to put the reaction curve function of B in A and we can solve the value for x A. So, in this case, we can find out x B is equal to 50 minus 0.25 x A. So, now, what we will do? We will put the value of x A in order to solve for x B. So, this is equal to 50 minus 0.25 by 95 minus 0.5 x B. So, that comes to 50 minus 23.75 plus 0.125 x B. So, solving for this x B will be equal to 30, x A is equal to 80 and putting a value of x A and x B that is 80 plus 30 that comes to 120 and putting the value of this, we will get the value of B which is equal to 45. So, this is the output of the B, this is the output of A and this is the profit maximizing level of output of A and B using the Carnot model or generally using the reaction curve approach. So, what we discuss in case of a Carnot model? This is a typical situation where two firms engage with each other, they know the interdependence, but they are not considering the fact that they are interdependent to each other in order to decide the output plan. And that is the reason when they are revising their plan, they are not considering the what will be the rival's reaction to the revised plan and ultimately they are reaching to a equilibrium which is stable, but in that case they are not exploring the output for the entire the market. And here we take the assumption that there is zero cost of production and we also discuss in case of Carnot model that when we assume the zero cost and there is a linear demand curve, the output of perfect the output of monopoly is half of the competitive output and the duopoly output is the two third of competitive output. So, to summarize this H per Carnot solution equilibrium is stable and each firm will be maximizing profit by selling equal amount of output at the same price. So, price same they are selling the equal amount of output like one third one third of the total market and equilibrium is reached when both the firm earns maximum profit and have no tendency to change their output. Then we will take the case of another non-colonial model that is generally known as the Stackelberg model and this is the extension of the Carnot model. And this is popularly known as the leader follower model and here one player is sufficiently sophisticated to recognize that the rival firms act according to Carnot assumption. So, here one player they feel that they recognize that rival firms what is the rival firms reaction and what assumption they are taking when they are revising their output plan. So, this sophisticated firm when they recognize that what will be the rival's plan or what is the reaction curve of the rival, they also able to incorporate that in their own profit function because they knows now what is the reaction curve function of the rival. They act as a monopolist, the nape firm will act as a follower. So, here how it is different from the Carnot model? Here in the case of Carnot model when the firm they were deciding about the output plan they are not considering the reaction function of the other firm. But in case of this Stackelberg model they consider this reaction at least one of the firm which sophisticated enough to understand or identify the reaction function of the other firm and they incorporate that in the profit function. And that firm who has identified this they generally act as the leader and the other firms act as a follower and that is why it is also known as the leader follower model this typical Stackelberg model. Both the firms is in equilibrium because they are maximizing the profit. Before going into this equilibrium we will see that ideally graphically how they reach to this equilibrium. So, this is the reaction curve of firm A and this is the reaction curve function of firm B. Now, this is the point where both the. So, this is the iso profit and this is another iso profit for B. So, this is x dash B and this is x dash A. Similarly, this is the iso profit function for A. This is also iso profit function of B. So, this is also the iso profit function of A. This is A, this is B. So, RB is the firm's B reaction function, RA is the firm A reaction function. Now, corresponding to this here we have xA and here we have xB. E is the equilibrium output. Now, let us assume that firm A is sophisticated enough and they operate in typically this RA, RA, E, RA because this is the reaction curve function and they will produce A which is profit maximizing because the iso profit curve is also in the reaction curve function now. Now, in this case A will produce OXA and B will produce OXB. In this case A is the leader and B is the follower. Now, suppose B is the sophisticated firm over here. What is the reaction function? Approach the reaction function is again RB E is the reaction function for firm B. It is equilibrium at the point B. So, B will produce OXB dash and firm A will produce OX dash A. So, if you look at whoever is sophisticated they are producing more, who is they are the leader, whoever is not sophisticated their follower they are generally paying, they are producing less. Like in case of in the first case B is producing less, A is producing more and in the second case B is producing more since B is the leader and A is producing less. Now, till the time the situation in one of them is leader the other is follower or the reverse may happen that B is the leader and A is the follower they will just the output will change because they are sophisticated. Now, what happens when both of them they become sophisticated? Price war will continue. What is the outcome? Price war will continue, but price war is also not beneficial for the oligopolys that also they know. So, initially when both of them they will be trying to sophisticated they will be trying to be the leader in the market. Initially price war will continue, but when they realize that price war is not going to benefit them rather price war is going to benefit the consumer. They will stop over there or they will stabilize price over there and then finally, they get into the cartel. So, Steckelberg model says what Steckelberg model says that it is always profitable if one of them is leader the other follower still the time the follower is also getting their share of profit and their share of output. But the question is that it will not continue for long run because if one firm is getting more profit because he knows that what is the reaction pattern of the other firm. The other firms will also try to do that in the long run and eventually both of them they were trying to be the leader and that will lead to the price war and finally, it is a cartel. So, the end outcome when you think about the end outcome of Steckelberg model still it is not determined fully that what should be the end outcome where they should stop. So, when it comes to monopolist both the firm this typically the steopolis both the firms in equilibrium because they are maximizing their profit and have no tendency to change the output typically in the graph if you have seen at the point E and equilibrium is reached when each firm is able to assess the other output correctly. And this is achieved after a series of change in the output by each firm in the anticipation of other outputs remaining unchanged. Like in the previous case in case of Karnat model we are discussing the action reaction pattern of both the firms finally, take them to the equilibrium and the same thing happen in case of Steckelberg model also equilibrium is reached when each firm is able to assess the other output correctly and this is not happened once this generally happens after the action reaction pattern and in the anticipation that the other outputs is remaining unchanged. Then before going into the next model we will just take a small numerical to understand this Steckelberg model. So, we have a demand function which P is equal to 200 minus Q. Then cost is fixed so MCA and MCB is equal to 80. So, P also we can say this is 200 minus 200 minus QA plus QB and what will be the revenue function of A. So, total revenue of A is P QA. So, this is 200 minus Q by QA which is 200 QA this no minus here 200 QA minus Q A QB because this Q is again QA plus QB. So, total revenue of A is 200 QA minus Q square A minus QA QB and for marginal revenue of A this is DTRA with respect to DQA. So, this is 200 minus 2 QA minus QB. Marginal cost of A is equal to 80. So, if marginal profit maximizing rule says that marginal revenue of A should be equal to marginal cost of A. So, 200 minus 2 QA minus QB should be equal to 80. So, QA is equal to 60 minus half QB and this is generally the reaction function of reaction function of reaction function of A. Similarly, for B we can find out QB is equal to I am not just getting into the detail of the derivation. So, QB is equal to 60 minus half QA. This is the reaction function of this is the reaction function of B. So, now to solve the value of Q and QB we can just put the value of QA in equation of QB or QB in equation of QA. So, QA is equal to 60 minus half QB. So, 60 minus half QA this is the value of QB. So, simplifying this we will get QA is equal to 40 and QB also is equal to 40. So, QA is equal to 40, QB is equal to 40 and Q has to be equal to 80 since it is QA plus QB and price is equal to 200 minus Q. So, 200 minus 80. So, 120. So, Q is equal to 80, V is equal to 120, QA is equal to 40 and QB is equal to 40 with this demand function and cost using the Stackelberg model. Then generally how general to solve this numerical or how to find out this profit maximizing level of output for both the firms. Using the profit maximizing rule we need to find out the reaction curve function for both the firms that is for firm 1 and firm 2 and from there we can solve the value of output that is QA, QB or Q1, Q2 just putting the value of the others and that gives us the total output in the market and also the output specific to the firm. So, here typically the reaction function generally we say that this is the reaction function approach through which generally we get the individual firms output and the total market output. Then we will get into the discussion of king demand curve model and king demand curve model is also one form of the non-collusive oligopoly model where it assume that there is no cooperation or no collusion among the firm in case of a king demand curve model. And this model generally explain us that why the price is rigid for the firms and at least in the oligopoly market why it changes very slowly over time. So, individual firms basically afraid to change their price because of what other firms might do. So, if one firm change the possibility that the other firm may not to change and that is the reason they afraid to change the price and that is the reason in case of oligopoly market maybe decreasing price is not so slow, but increasing price is slow because others may not follow to this. There are certain assumption we take in order to understand the king demand curve model. The first one if a firm raises price other firms own follow and firm loges a lot of business. So, whenever there is a increase in the price the other firm will not follow it automatically and that is why that firm who has raised the price they generally lose lot of business. So, demand is very responsive or elastic to price increase and if a firm lower the price other firm follow, but the firm does not gain much business. So, in this case if you look at this part of the demand curve is inelastic because whenever one firm lowers the price the other firm also lowers the price in order to get more market share or more demand and that is why in this case the change in the price is not affecting the quantity demanded of the firm much and that is why we get an inelastic demand curve. So, demand is very responsive or the elastic to increase in the price and demand is fairly unresponsive and inelastic to price decrease. So, if you look at this graph if reduce price and competitor match the price typically if you look at now we are getting two set of the demand curve. One is the elastic demand curve another is the inelastic demand curve. If reduce price and competitor match the price cut then move along the inelastic demand curve that is segment D i and if increase in the price and competitor is not following that then we get in the segment of the elastic. So, we have two kind of demand curve now. One we have a inelastic demand curve and we have a elastic demand curve. So, this inelastic demand curve is when price decreases other firm also decreases the price and elastic is the basis is that whenever there is a increase in the price other firm keep the price constant. So, ideally what will be the demand curve for the firm? There are two segment one and one segment of the elastic demand curve and one segment of the inelastic demand curve. So, this segment of the elastic demand curve because of the fact that whenever there is increase in the price the competitor they are not matching to it and this part of the demand curve is one whenever the price cut happens the other firms or the competitor also decreasing the price. So, increase in the price competitor price remain constant decrease in the price the competitor also decreasing the price that is why the demand curve of the firm has two segment one is the elastic segment with respect to increase in the price and other is the inelastic segment that is the with respect to decrease in the price. Here to remember that decrease in the price is generally followed by the competitor, but increase in the price is not followed by the competitor and that is why we get two separate segment in the demand curve one is the elastic segment and other is the inelastic segment. So, this is generally the shape of the king demand curve where the upper portion is elastic and the lower portion is inelastic. The upper portion is come from the elastic demand curve and in this segment whenever there is a increase in the price because increase in the price the competitor they are not going to follow it and the downward segment is the part of the inelastic segment where whenever there is a increase in the decrease in the price competitor generally follows this. Now, how this marginal revenue curve here we get? This is the first case we get also two marginal revenue curve here because since we have two demand curve we have two marginal revenue curve. The first segment of the marginal revenue curves comes from the top part of the demand curve which is the elastic demand curve. So, here this marginal revenue curve with respect to the elastic segment of the demand curve. Then we will see what is the marginal revenue curve for the bottom segment and for the marginal revenue curve for the bottom segment is again it is a part of the inelastic demand curve. So, if you will find there are two marginal revenue curve with respect to two demand curve because it is one demand curve, but it has two segment one is the elastic segment other is other one is the inelastic segment. So, one marginal revenue curve with respect to the elastic segment and the other marginal revenue curve with respect to the inelastic segment. So, this is for the bottom part of the demand curve and previously it was the top part for the demand curve. So, this is the inelastic part of the demand curve. So, this is generally the king demand curve and we have two marginal revenue curve. If you notice here there is a gap between the two marginal revenue curve why there is a gap between two marginal revenue curve because our demand curve has a kink and at the point of kink we are not able to decide which one is the marginal revenue curve. So, if you look at demand curve is generally known as a king demand curve because it has a kink between the two segment of the demand curve that is between the elastic segment and inelastic segment of the demand curve. Corresponding to the elastic segment we have one marginal revenue curve corresponding to the inelastic segment we have another marginal revenue curve. At the corresponding to the point of kink there is a gap between the marginal revenue curve one and marginal revenue curve two. So, that is why in case of a king demand curve there is a gap between the marginal revenue curve one and marginal revenue curve two. Now, the question comes how the marginal cost should be because we need to get the equality between the marginal revenue and marginal cost to get the profit maximizing level of output. And the marginal cost should cut which segment of the marginal revenue curve whether the segment related to the elastic demand curve or whether the segment related to the inelastic demand curve. So, marginal cost generally intersect the marginal revenue curve in the gap in the vertical segment in the gap between the marginal revenue one and marginal revenue two. And whenever there is a increase in the marginal cost if the cost shift up slightly, but marginal cost still intersect the marginal revenue in the vertical segment there will be no change in the price. Because if any point of time if marginal cost goes to marginal revenue one that is elastic segment or to the inelastic segment still it will not consider as for the whole demand curve whole king demand curve. And that is why you will find there is a price rigidity and this is the outcome of the price rigidity that we get to level of marginal revenue curve and the marginal cost curve is not going for the marginal revenue one or marginal revenue two rather it is in the gap. So, even if there is a increase in the cost till the firm is not changing the price because if it changing the price again it may lead to a situation that the other firm will not follow it and they will get into the loss. So, king demand model generally it provides the explanation detailed description of firm under oligopoly and it explains the various characteristics such as price rigidity why there is a indeterminate demand curve, non-price competition and independent decision making. But this model fails to explain a basic question how price is determined because it is it is really a fuzzy when the price is decided in the gap in the vertical segment between marginal revenue one and marginal revenue two. And that is why this model has a criticize on the ground that it fails to explain the basic question of any model that how the price and output is determined because we have a king demand curve we have two level of marginal revenue curve that is marginal revenue one and marginal revenue two. So, we will just take a numerical to understand that when you take a numerical when you take a real production function when we take a real demand function cost function whether we get the gap between the marginal revenue one and marginal revenue two with respect to two different demand and whether the marginal cost also pass through the vertical segment or the gap between the marginal revenue one and marginal revenue two. So, we will take two demand function we will take as Q 1 and we will take as Q 2. So, we have two demand function one is 28 minus 4 P 1 and second is 10 minus P 2 we will take a total cost function that is 1 4 Q square plus Q plus 50 and we need to find out the marginal revenue marginal revenue for both the firms marginal cost price output and we need to say what is the upper and lower limit of MR because that will tell us whether there is a vertical segment or gap between marginal revenue or not and whether MC falls in the gap of 2 MR or not. So, to start with we will find out since we have Q 1 is equal to 28 minus 4 P 1 and we will find P 1 is equal to 7 minus 1 by 4 Q 1 Q 2 is equal to 10 minus P 2. So, P 2 is equal to 10 minus Q 2 total revenue one is P 1 Q 1. So, that comes to 7 minus 1 by 4 Q 1 square and total revenue on corresponding to this will get the marginal revenue one that is 7 minus half Q 1. Similarly, total revenue 2 is P 2 Q 2. So, this is 10 Q 2 minus Q 2 square marginal revenue 2 is 10 minus 2 Q 2 and we have now marginal revenue 1 we have now marginal revenue 2. We will find out the marginal cost from our total cost function so, total cost function is 1 4 Q square plus Q plus 50. So, marginal cost will come as 1 plus half Q and if you look at the king at the point of king both the demand curve should intersect and to get this intersection we have to do is equal to Q is equal to Q 1 plus Q 1 equal to Q 2. So, 7 minus 1 4 Q is equal to 10 Q. So, Q is equal to 4 and P is equal to 6. So, taking the value of Q and P marginal revenue 1 is equal to 7 minus half into 4 that is equal to 5, marginal revenue 2 is equal to 10 minus 2.4 that is 2. So, marginal revenue 1 is 5, marginal revenue 2 is 2. Now, we need to find out MC. So, MC is equal to 1 plus half Q. So, this comes to 1 plus half multiplied by 4. So, this comes to 3. So, we can say that Q is equal to 4 this is the output P is equal to 6. We have first segment of MR is equal to 5 the value of second segment of MR is equal to 2 and MC is equal to 3. So, we can also prove that the MC falls in the gap of 2 level of MR that is marginal revenue 1 and marginal revenue 2. So, today we discuss about typically in this session we discuss about the Cournot model, Stackelberg model and King demand curve model and all these 3 models are part of non-collusive oligopoly model. In the next session we will discuss about the collusive oligopoly model typically the cartels and the price