# Help with calculus question in economics

• Nov 6th 2011, 12:02 PM
russellmania79
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 e ect 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?

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!
• Nov 6th 2011, 12:46 PM
skeeter
Re: Help with calculus question in economics
Quote:

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?

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
• Nov 6th 2011, 01:46 PM
russellmania79
Re: Help with calculus question in economics
Thanks for getting back to me. I'm still a little confused though. What happens to the 2 in front of the BP?
• Nov 6th 2011, 02:19 PM
skeeter
Re: Help with calculus question in economics
Quote:

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)