1 suppose that the demand curve for a good is given by dp...

1. Suppose that the demand curve for a good is given by D(P) = 100/P, what price will maximize revenue? 2. If D(P)=12 -2P, what price will maximize revenue? 3. If the market demand curve is D(p) = 100 - 0.5P, what is the inverse demand curve? 4. Show that when the elasticity of demand is equal to one, the marginal revenue of producing an extra unit of a good is zero.

Transcript

00:01 Hello students we are given our question suppose that the demand curve for a good is given by this function okay what price will maximize revenue so we can start with first part we are given here that the what we are given the dp is equal to hundred divided by b we can check again that divided by p so here we are supposed to do know that the total revenue total revenue can be written as price times quantity demanded okay so tr will be t times of quantity demanded it means demand so hundred divided by p which comes out as equals to totally hundred now when we here what we need to do the total revenue the total revenue will be maximum will be maximum when we can write the derivation of total revenue have to will be zero okay so we can write here d t r divided by dp is equal to zero so here we are supposed to know that the d of hundred by dp will obviously zero because the differentiation of constant term is nothing but equal to zero so we can say that hence any price any price will maximize will maximize revenue okay students now we will go to our basically second part what we are asked if a demand curve is given as 12 minus 2p what price will maximize revenue so we are given the demand function as dp is equal to 12 minus 2p okay students first of all we need to find again that total revenue which is pq so here we can just write t r is equal to p times of q is given as 12 minus 2 p we can write here tr is equal to 12p minus 2p square.

02:09 So here when we differentiate this term, what we will get 12 minus 2 to the 4.

02:14 Okay, in order to find the maximum value of total revenue, what we need to do? we just need to make it equal to 0 dtr by d .p is equal to 0.

02:25 So 12 minus 4p have to be equal to 0.

02:29 4p equal to 12.

02:30 Basically p equal to 12 divided by 4...

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