Thread: Help with calculus question in economics

Hi guys... Not sure if this is the right forum to post my question in but i'll give it a go anyways.
Here's the question:
Total Revenue is price times quantity. Suppose the demand curve for a good is
given by Q = A BP . Find the eect of a price change on revenue, i.e., take the
derivative of revenue with respect to price. When is it positive? When is it negative?
What role does elasticity play?

Here is the answer:
Q = A - BP . So, R = PQ = AP - BP^2. This is total revenue. Taking
derivatives with respect to price, dR/dP = A -2BP = Q - BP (since Q = A-BP ).
Note that elasticity is E = (dQ/dP )(P=Q) = B(P/Q). So, EQ = BP .
Substituting this in the expression obtained earlier, we have, dR/dP = Q
BP = Q + EQ = Q(1 + E) = Q(1- absolute value of E).
The RHS is positive if demand is inelastic and negative if demand is elastic.
So, if demand is inelastic an increase in price will increase revenue and if demand is
elastic an increase in price will decrease revenue


Now the part im stumped with is if dR/dP = A-2BP, how does that = Q-BP (since Q = A-BP)? Any help would be greatly apreciated. Thanks!

Originally Posted by russellmania79

Hi guys... Not sure if this is the right forum to post my question in but i'll give it a go anyways.
Here's the question:
Total Revenue is price times quantity. Suppose the demand curve for a good is
given by Q = A BP . Find the eect of a price change on revenue, i.e., take the
derivative of revenue with respect to price. When is it positive? When is it negative?
What role does elasticity play?

Here is the answer:
Q = A - BP . So, R = PQ = AP - BP^2. This is total revenue. Taking
derivatives with respect to price, dR/dP = A -2BP = Q - BP (since Q = A-BP ).
Note that elasticity is E = (dQ/dP )(P=Q) = B(P/Q). So, EQ = BP .
Substituting this in the expression obtained earlier, we have, dR/dP = Q
BP = Q + EQ = Q(1 + E) = Q(1- absolute value of E).
The RHS is positive if demand is inelastic and negative if demand is elastic.
So, if demand is inelastic an increase in price will increase revenue and if demand is
elastic an increase in price will decrease revenue


Now the part im stumped with is if dR/dP = A-2BP, how does that = Q-BP (since Q = A-BP)? Any help would be greatly apreciated. Thanks!

dR/dP = A - 2BP = (A - BP) - BP = Q - BP

Thanks for getting back to me. I'm still a little confused though. What happens to the 2 in front of the BP?

Originally Posted by russellmania79

thanks for getting back to me. I'm still a little confused though. What happens to the 2 in front of the bp?

-2bp = -(bp + bp)