 So, we will continue our discussion on monopoly like what we discussed in the previous class like short non long run output and price and output decision in the monopoly, how the farms gets profit, normal profit, super normal profit or incur loss and then also we check the demanded revenue, what are the different entry barrier, what are the sources for barrier to entry, what are the different types of monopoly, what we checked in the last class. So, if you remember we talked about the feature of monopoly first, what are the different characteristic of monopoly. Then we discussed about the regions and types of monopoly, then we discussed about the demand marginal revenue for a monopoly firm and then we talked about the price and output decision in the short run and in the long run. So, if you remember in the short run maybe the farm gets normal profit, super normal profit incur loss, but generally in case of long run the farm never incur loss, rather they try to get at least the normal profit even if not the super normal profit. So, in this particular session we will talk about the supply curve of a monopoly firm, then we will take a case of a multi plant monopoly and we will see how the price and output decisions are made in case of a multi plant monopoly. Then we will talk about the impact of change in the demand and cost, then we will talk about the imposition of tax, who gets the bottom of tax whenever there is a imposition of tax whether it is buyers and sellers. Then we will talk about the different methods or measures of monopoly power and then we will talk about the welfare cost of monopoly. So, to start with we will start our discussion the supply curve of monopoly. So, if you remember in case of a perfect competitive firm the supply curve is that segment of marginal cost which lies above the minimum point of average variable cost, consider as the supply curve for the competitive firm. Now, why that is consider as the supply curve of competitive firm because the firm shutdown the operation if price goes below the minimum point of AVC and that is the reason the minimum point AVC is consider as the starting point for the firm supply function and that is the reason the supply curve starts from that point of the marginal cost. So, it is the above segment of the marginal cost which lies above the average variable cost is generally known as the supply curve for the competitive firm. The situation is different in case of monopoly firm. Now, let us see what we consider as the supply curve in case of a monopoly firm whether there is a existence of supply curve or there is no existence of supply curve in case of a monopoly firm. So, the intersection of a monopolist marginal revenue and marginal cost curve identify the profit maximizing quantity if the price is found on the demand curve. So, if you remember our MCMR rule that gives us once we follow the MCMR rule we get the profit maximizing output and profit maximizing price and the price generally found on the demand curve. Thus, there is no curve that shows both price quantity supply and there is no monopolist supply curve. But if you look at now how the supply of goods whatever decided by the monopolist where it gets represented. So, supply of goods by the monopolist at a given price would be determined by both market demand and the marginal cost curve. So, there is no definite supply curve for a monopolist because the whatever the supply of goods by the monopolist at a given price would always be dependent on the market demand and the marginal cost function. Since it is a single seller single firm they always look for the profit where they always look for the price which goes above the marginal cost. So, that they can maximize the revenue and they can maximize the profit because in case of monopoly if you find it is not that P is equal to MC rule the price is always greater than the marginal cost. Whereas, in case of perfect competitive firm it is always P there is a equalization of P is equal to MC that leaves the that leaves no scope for the profit up to maximize the profit for the individual firm. Since supply curve is absent. So, basically it is the demand and MC curve they plays a greater role when it comes to the price and output decision of the monopolist firm. Now, we will take a different type of case that is the case of a multi plant monopoly and what is multi plant monopoly? Multi plant monopoly is one where the firms produces the same product, firms produces the homogeneous product in different plants at different cost of production. So, if the firm has to produce 100 units of the particular quantity of product he can produce it in 2, 3 different plants where the cost of production the per unit cost of productions are different different in some cases it is higher and some cases it is lower. So, when the firm produces the homogeneous product in 2 different plant each with different cost the multi plant monopolist has to decide also and how to allocate the profit maximize output between 2 plants. So, the product is homogeneous but the plant is producing the homogeneous product the same product or the identical product in all the on the different plants and obviously the plant each plant is having a different cost function they are not operating at the same cost function or they are not operating at the same level of cost that implies that the per unit cost has to be different in the different plant. So, now let us see how the price and output determination is generally done when it is a case of a multi plant monopolist and the entire situation is called as the multi plant monopoly. So, in this case the firm must determine how to distribute the production between both the plants which firm should produce how much and because it always dependent on the cost of production. So, firm must determine how to distribute production between both plants production should be split. So, that marginal cost in the plant is the same and output is chosen where m r is equal to m c and profit is therefore, maximized when m r is equal to m c at each plant. So, productions will be split. So, that the marginal cost of the plant is the same the per unit cost added to the total cost by producing one more unit should be same and output is chosen on the basis of the same marginalist rule that is marginal cost has to be equal to the marginal revenue and profit is maximized at the by following this equalization rule that is marginal revenue equal to the marginal cost at each plant. So, we will get two set of marginal revenue curve and we will get or we will get two set of marginal revenue curve and two set of marginal cost curve and when it comes to the profit maximizing level in the both plant the m c m r has to be different because the cost is specific to the plant whereas, the revenue is specific to the firm is a whole. So, if you consider here q 1 is the output c 1 is the cost of production for plant 1, q 2 and q 2 is the output for plant 2 and c 2 is the cost of production for plant 2. Now, what is the total output? The total output has to be q 1 plus q 2 and in this case what will be the profit? The profit is the revenue what the firm gets that is p q 2 minus c 1 q 1 that is the cost function of the first plant and c 2 q 2 that is the cost function of the second plant. So, firms should increase the output from each plant until the additional profit from last unit produced plant 1 equals to 0. So, the firm is going on increasing the output production of the output in each plant till the time there is a positive profit comes to the firm. Once the profit goes to 0 then the firm generally stops increasing output in that plant because if after that it may happen that the profit goes in the negative side. So, this is the profit maximization we take the change in the profit with respect to change in the q 1 that is change in the revenue minus change in the cost function of the first plant and change q that is again MR if you look at the first term is generally MR because that is change in the revenue with respect to change in q 1 and second part is generally m c 1 that is the specific cost function for the plant 1 and h per the marginal rule it has to be equalized to 0. So, marginal revenue minus marginal cost 1 is equal to 0 marginal revenue equal to and marginal revenue and that again if you simplify this then the marginal revenue is equal to the marginal cost for the plant that is m c 1. Now, the same thing we can do it for the plant 2 and what we will get for plant 2 that is the marginal revenue has to be equal to the m c 2 that is the cost function marginal cost function for the plant 2. Now, firm should choose to produce where marginal revenue is equal to marginal cost 1 and marginal cost 2 and we can show this graphically like marginal revenue and marginal cost it gives the total output and this point shows marginal revenue for each firm and where marginal revenue crosses the m c 1 and m c 2 shows the output for each firm. So, now we can see graphical representation of this multipland monopoly generally how it happened how the price is decided on the basis of them. So, if you look at here the equilibrium quantity equilibrium price is decided on the basis of the total revenue and total cost of both the plants, but when it comes to how much they have to produce and because they do not have the control on the price only they have a control about the how much they have to produce in each plant that is again comes from the fact that marginal revenue is equal to m c 1 following the marginalist rule and marginal revenue for equal to m c 2 for the plant 2 again following the marginalist rule. So, this is our average revenue curve, this is the marginal revenue curve, this is our average cost curve, this is the marginal cost curve, this is the point where marginal revenue and marginal cost intersect each other. From here we can find out the equilibrium quantity and equilibrium price. So, this price has to be followed in both the firms so this is again p is equal to m r and p is equal to a r and here it is again p is equal to a r. Now, we will see how we get it from how this q is divided between plant 1 q 1 and q 2. Now, suppose we have a average cost rate here, we have a marginal cost rate here. Now, this is the point where there is a equalization of the marginal cost and marginal revenue. Since we have only one marginal revenue, but we have two level of cost of cost production. So, we will equalize m r with m c 1, we will equalize m r with m c 2. So, corresponding to this we get a point here that is and this gives us the marginal revenue equal to the marginal cost 1. And corresponding to this, this is the output level that has to be produced by plant a. Whereas, if you look at again we have a different cost function for plant 2 and this is average cost 2, this is marginal cost 2, this is average cost 1, this is marginal cost 1. Similarly, again we will take a point corresponding to the marginal cost and marginal revenue and this gives us the output for plant 2. So, this q is equal to q 1 plus q 2 plus and generally how this output is decided? Initially the total output, this profit maximizing output q is decided on the fact that marginal cost which is some total of marginal cost 1 and marginal cost 2 is equal to marginal cost. On that basis, this following the marginal is principle, marginal cost, marginal revenue on that basis this is the equilibrium level of output and this is the equilibrium price. The same price is, same price has to be followed for plant 1, plant 2. How plant 1 and plant 2 they are different from each other? Plant 1 operate at a lower cost of production and plant 1 is operate at a higher cost of production because average cost 2 is higher than average cost 1 and similarly corresponding to that we get two different level of cost function that is m c 1 and m c 2 and m c 1 when you equalize with m r we get the level of output that is going to be produced by plant 1 corresponding to m c 2 when you equalize the m c 2 with m r we get the q 2 which is the same level again the level of output that is going to be produced by plant b. Now, the question comes what is the logic over here on what basis generally the firm produces more? Obviously, the firm produces more in that plant where the cost of production where the average cost of production generally at a lower level because through that they can they get the economies of scale when they operate the scale of product and when they expand the scale of operation they expand at a lower cost of production and that is the reason they prefer to produce more in a low cost firm rather in a high cost firm because if they are producing in a high cost firm they are producing more in a high cost firm the cost of production the gap between the cost of production and the market price that generally narrow down and market price is same for that whether the output gets produced from the plant 1 or output get produced from the plant 2. And this is how the multi plant monopolist generally decides it is the same thumb rule what we apply for the profit maximizing level of output the monopolist firm the multi plant monopolist firm generally takes a total of marginal revenue for across the firm for across the plants and then they take the marginal cost which is the summation of marginal cost 1 for plant 1 and marginal cost 2 for plant 2 since there are 2 plants there may be many plants and always the marginal cost is the summation of marginal cost function of the all the plants where the output gets produced. So, after getting the summation of all this now it is get equalized with marginal revenue and corresponding to that we get a profit maximizing level of output and this profit maximizing level of output generally gives us the total quantity that has to be produced by the firm. Now firms decide the now firm divides the total output among all the firms on the basis of their cost of production. If it is low cost of production generally the firm prefers to give them more output to produce to get produce and if it is a high cost firm they generally produce at a produce less because the per unit cost is on a higher side. Then we will take a numerical to understand this that how this Q gets divided between 2 plants or how the profit gets firm we can find out with the help of a numerical. So, demand function is 200 minus x we have 2 plants m and n. So, this is the total cost of function for m this is the total cost function for n. So, total cost function for m is 30 x m and total cost function for n is 0.5 x n and the total cost function for n is 0.5 square. Now this x is output x is the output this is equal to the x m plus x n because this the output gets from both the firms that is x m plus x n. Now we will find out the output level what output to get produce what is the amount of x and we will find out what is the revenue and what is the profit. So, if you look at then now we have to find the total revenue and total revenue is 200 x minus x square because this is basically the P Q. Marginal revenue is equal to 200 minus 2 x m c 1 is equal to 30 and m c 2 is equal to x n. Now to find out what is the value of x m and x n what we should do now we should equalize the m c 1 may be that is you can call it m c m and this is m c n also. So, marginal cost for m marginal cost of n has to be equal to marginal revenue that is m r. Now when we equalize this m c m and m c n then we get x n is equal to from this 2 we get x n is equal to 30 and from m c 1 and m r what is our m r m r is 200 minus 2 x it has to be equal to what is m c m that is 30. So, 2 x is equal to 170 x is equal to 85. So, x is always a summation of x m plus x n. So, that way if x is 85 and x m is not known and x n is 30 then we can say that x m is equal to 0. So, the total output to be produced is 85 and among this 85 x n has to be produced by x n has to be produced plant n has to be produced 30 and plant m has to produce 55 units of output. Now what is the price once we get this what is the price to in order to find out the price now you remember your demand equation that is 200 minus x. So, that comes to 200 minus 85 which is equal to 115. So, we have the value of p we have the value of q in term of x and from there we can once we put the value of p and q in our revenue function and cost function we can get the value of the profit what the firm gets and please remember this profit is from both the plant that is plant m and plant n because the both the output all the output gets aggregated between both the plants to produce the it in the but when it comes to the firm it is when it comes to the firm the finish could always the price is same and the revenue goes to the firm that is also same irrespective of it whether it is produced in the plant m or whether it is produced in plant n. Next we will see what is the effect of shift in the demand on monopoly whenever there is a change in the demand how it generally affects the monopoly equilibrium or how generally it affects the monopoly profit or how it affects the equilibrium price and equilibrium quantity of monopolist firm. So, an upward shift in the demand curve that is increase in the demand curve marginal cost curve remaining the same will increase the equilibrium output level. So, m c remain same upward shift in the demand curve. So, generally average revenue shifts off. So, equilibrium output will increase and effect on the equilibrium price remain indeterminate. So, it is difficult to predict whether the price has to increase equilibrium price has to increase whenever there is a upward shift in the demand curve whether it has to be decrease or whether it has to be remain constant. So, we will check in which case it may increase in which case it may decrease and it which case it may remain constant. So, we are just taking one case here where we are saying that demand is upward. So, demand is increasing. So, suppose this is your d 1 this is d 0 or this is you can call it is m r 1 this is d 0 and this is m r 0 this is the marginal cost. So, we have one point here one point here. So, showing this point to understand more clearly. So, this is demand. So, initially we can consider the quantity over here we can consider the price and m r over here. So, initially the demand curve is d 0 marginal revenue curve is m r 0. What is the corresponding equilibrium point? The equilibrium point is the equation of marginal 0 and marginal cost and we get the point e 0, e 0 as the equilibrium point. Increase in the demand takes place from d 0 to d 1. Correspondingly we get a new level of marginal revenue curve and that the new point of marginal revenue curve again it is the equilibrium point we get as e 1. So, with the increase in the demand also if you look at still the price is constant even if the output is increasing from q 0 to q 1, but the price remains same at p 0 which is also equal to 0. So, in this case what we can say we can conclude that if the demand is increasing if there is a upward increase in the demand correspondingly there is a shift in the marginal revenue curve, but the position of the marginal cost curve is such that even if due to change in the demand the new equilibrium is taking place and the corresponding to new equilibrium we are getting a new level of output, but we are not getting a new level of price. The price remain constant only the output changes. So, if you look at it all more to on the shape of the marginal cost curve that will decide whether with the increase in the demand the equilibrium price will increase, decrease or constant. So, this is the first case where the price is constant whenever there is a increase in the demand from d 0 to d 1. Then we will take a case where the marginal when there is a increase in the demand function that generally increases the price also along with the change in the equilibrium output. So, this is d 0 this is marginal revenue 0 demand increases from d 0 to d 1. So, marginal revenue is also we get a new marginal revenue curve corresponding to new demand curve. This is the marginal cost curve. So, we get point E 0 which is the equation of the marginal revenue and corresponding to we get the equilibrium point E 0 and we get another point E 1 which is equalization of M R 1 and M C. So, we get another point of the we get another point of equilibrium. So, in this case in the first case this is the quantity profit maximizing quantity this is the profit maximizing price. After increase in the demand corresponding to new level of equilibrium this is the output and this is the price. So, in this case what is the outcome? The outcome is when the demand is increasing and correspondingly that M R is also increasing the in this case the price is increasing equilibrium price is increasing and also equilibrium output is increasing. So, if equilibrium price is increasing that is all to do with the shape of the marginal cost curve because marginal cost is increasing and if you look at the per unit cost cutting added to produce more output because of in response of demand is increasing and that is the reason the price is increasing due to change in the demand. Then we will take a case where there is a decrease in the equilibrium price whenever there is a increase in the demand for the product this is. So, d 0 is the initial demand curve, marginal revenue 0 is the initial marginal revenue with respect to the demand curve, d 1 is the change in the demand curve because of there is upward shift in the demand curve, marginal revenue is the change in the marginal revenue is the change in the marginal revenue with respect to d 1. Now, we will see how this leads to a decrease in the demand. We have one point again where we get the equation of marginal revenue 0 equal to marginal cost and we get E 0 corresponding to that we get the price is P 0 and quantity is Q 0. Then we get a new equilibrium that is marginal revenue 1 which is equal to marginal cost and we get the equilibrium point as E 1 corresponding to that we get as Q 1 and we get as P 1. So, equilibrium price is P 1 and equilibrium quantity is Q 1. So, in this case what is happening in this case the outcome is when there is a increase in the demand from D 0 to D 1 the equilibrium output is increasing and, but the price is decreasing. So, here if you can see the difference also in the previous two cases the change in the output is not very high as compared to this because relatively here the change in the output is also more because this the increase in the demand and that leads to decrease in the price which again leads to the increase in the output and if you look at this again follows the basic demand supply condition generally it happens in case of a open market or in case of a market which is competitive.