 Hello and welcome to the session. In this session we are going to discuss average and marginal revenue. First let us recall by demand function. The price per unit P can be expressed as a function of x that is P is equal to f of x. Now if r is the total revenue collected by selling x units then r is equal to P into x and the revenue function r which is equal to r of x is equal to P into x or we can also write it as x into f of x as P is equal to f of x. Now average revenue can be defined as the revenue per unit of a commodity and is denoted by a r that is average revenue is the revenue received per unit. Therefore average revenue is equal to total revenue upon number of units sold which is equal to r upon x which implies that average revenue is equal to r upon x that is P into x upon x as r is equal to P into x. Therefore we have average revenue is equal to P that is average revenue is same as the price per unit. Let us take an example the total revenue received from the sale of x units of a product is given by r of x is equal to 15x minus 0.25x square finds average revenue. Here we are given the revenue function r of x is equal to 15x minus 0.25x square that is rx is given as 15x minus 0.25x square and we know that average revenue that is a r is equal to r upon x which implies that a r is equal to 1 by x of 15x minus 0.25x square. Therefore average revenue is equal to 1 by x into 15x that is 15 minus of 1 by x into 0.25x square that is 0.25x. So average revenue is given by 15 minus 0.25x. Now we shall discuss marginal revenue. It is defined as the rate of change of total revenue with respect to the quantity sold. It is denoted by mr and mr is given by d by dx of r that is the total revenue. So mr is equal to rate of change of total revenue with respect to the quantity sold and we know that total revenue is equal to p into x. Therefore we have mr is equal to d by dx of p into x. Now applying product rule here we have p into d by dx of x that is 1 plus x into d by dx of p and we can also write it as mr is equal to taking p common from both the terms we have p into 1 plus x upon p into dp by dx. Let us take the same example. The total revenue received from the sale of x units of our product is given by r of x is equal to 15 into x minus 0.25 into x square. Find the marginal revenue. The revenue function is given as r of x is equal to 15 into x minus 0.25 into x square and we know that marginal revenue is equal to d by dx of r. Therefore we have mr is equal to d by dx of r that is 15 into x minus of 0.25 into x square which is equal to d by dx of 15x minus of d by dx of 0.25x square which is equal to d by dx of 15x that is differentiating 15x with respect to x we get 15 minus of differentiating 0.25x square with respect to x we get 0.25 into twice of x. Therefore we get 15 minus 0.5x marginal revenue mr is equal to 15 minus 0.5 into x. Now let us discuss the conditions under which a firm operates and there are two such conditions. First is pure competition. Here involves many firms in similar business activity that is production and marketing of the same product or products the market determines the price and not the producer. Here the price of a commodity is independent of the level of output x so total revenue r is given by p into x and marginal revenue mr is equal to p plus x into dp by dx and here marginal revenue mr is equal to p as p is constant therefore dp by dx is equal to 0 where p is price per unit and the second condition we harvest monopoly where there is no competition then the business is said to operate as a monopoly business Here the price of the commodity depends upon the number of items produced and sold here demand depends on price and price depends on demand here is only one seller and Note the substitute of the commodity marketed by this seller this completes our session hope you enjoyed this session