• What is relationship between total revenue (TR) and total...

• What is relationship between total revenue (TR) and total variable cost (VC) if the price is equal to the AVC (the price is tangent to the minimum AVC), (is TR greater, less, or equal to VC)? What do we call this point (that is when the demand curve is tangent to the minimum AVC)? Remember, the price is the demand curve. • What is relationship between total revenue (TR) and total variable cost (VC) if the price is between AVC and ATC (does TR cover part of VC, AII VC or all VC and part of foxed cost)? choose one of the options. • What is relationship between total revenue (TR) and total cost (TC) if the price is equal (tangent) to the minimum) ATC (is TR greater, less, or equal to TC)? Choose only on option What do we call this point? • What is relationship between total revenue (TR) and cost (TC) if the price is greater than ATC (is TR greater, less, or equal to TC)? Does the firm make positive economic profit or loss?

Transcript

00:02 We would want to be telling you about how to calculate or how to maximize total revenue okay so in order to find out or to to find out the output so in order to find out the output at which our total revenue becomes maximum what we will do we'll take the derivative of total revenue with respect to the quantity wrt denotes with respect to okay and we'll set this equals to zero since we have given over here as total revenue equals 250 q minus 2 q square okay now taking the derivative of this that is dtr by dq what we'll get we'll get 250 minus 4 q okay now putting set this equation equals to zero what we will get and solve for the value of q we will get 250 minus 4 q equals to 0 4 q equals to 250 from here we get q equals to 250 divided by 4 which comes out to be 62 point five so this is the output at which the total revenue will be maximum which is sixty two point five units is it clear now in the second part that we need to calculate here is to maximize the sales revenue so in order to maximize sales revenue in order to maximize sales revenue we need to find out the quantity q this is the output quantity q that maximize sales revenue given the demand schedule as p equals to 90 minus 0 .3 okay what we'll do first we will substitute this price function into the revenue function which is sales revenue is pq okay now putting the value of p over here we'll get what sales revenue equals to 90 minus 0 .3 q whole times q that this quantity on solving it we will get 90 q minus 0 .3 q square in order to maximize sr we'll take the derivative of sr with respect to the quantity okay and set this whole equation equals to 0 and we'll find the value of q so the firm needs to sell 150 units now third part is to find marginal revenue to find to find marginal revenue when quantity is 100 for this what we'll do we will find the derivative of total revenue function which is total revenue given as 600 q minus 0 .5 q square taking the derivative of the dtr by dq okay we will get how much 600 minus q okay now we'll put the value of q that is 100 in this equation so we'll get marginal mr equals to 600 minus 100 which comes out to be 500 clear now second part that we need to find out is to find when total revenues at its maximum okay so first what we'll do again we'll take the derivative of total revenue total revenue function is given as 600 minus 0 .5 q square taking the derivative of this with respect to q we'll get 600 minus q putting this equals to 0 so we'll get 600 minus q equals to 0 from here we'll get q is equals to 600 those total will be maximum when quantity is 600 clear now third part that we find out to find out the price the firm should charge to achieve the maximum total revenue okay for this what we'll do we will put the value of q which is 100 which is 600 into the demand function okay so we have price equals to 90 minus 0 .3 q so 90 minus 0 .3 in place of q we'll put 600 on solving it we'll get 90 minus 180 which comes out to be minus 90 so from here what we get we conclude that the firm should not charge a negative price so it's important to check the context of the problem to ensure that the price calculation is meaningful clear the next part of the question says to maximize sales revenue for the nonlinear demand schedule which is given as p equals to 750 minus 0 .1 q square so what will do first we will take the derivative and sets it equals to equals to 0 and we'll solve for q okay that is how we will calculate and similarly for the next part which says that to show that tr is maximum when quantity is 18 for the nonlinear demand schedule p equals to 194 .4 minus 0 .2 q square here also what we'll do we'll take the derivative of tr and equals 0 at q equals to 18 and we'll follow the same steps as we did in question number one of this okay now the next part of the question says us to maximize profit and then we'll equal it okay given the demand function let's calculate the marginal cost with respect to the total cost total cost is given as 40 plus 30 q plus 0 .4 q square so mc will be derivative of tc with respect to quantity q okay on solving it we'll get mc will be 30 plus 0 .8 q similarly we'll find out mr which is total revenue which is the price quantity okay using the demand schedule and this comes out to be 190 minus 0 .6 q we have already calculated this now equating both the equation that is mc is equals to mr we'll get 30 plus 0 .8 q equals to…

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