Thread: Elasticity question: Finding maximized price.

The consumer demand curve for cases of gadgets is given by , where p is the price per case and q is the demand in weekly sales.

a) If the gadgets cost $30 per case to produce, use calculus to determine the price that should be charged per case to maximize the weekly profit.

I know how to find revenue but the $30 in the equation's throwing me off. On my answer key the answer is $50 per case but I keep coming up with $45. Here's what I am doing:









I am sure it's something silly considering I am neglecting to incorporate the $30 into the picture but that's what 6 hours of studying at 3am will do to you!

What you want to do is find the profit, subject to there being a positive demand (price<90) which would be

Profit=Revenue per week - Cost per week







Find stationary values by taking the first derivative of the profit function and setting it to 0, remembering the above condition then confirm which of the answers is a maximum by finding which would make the second derivative negative

Originally Posted by thelostchild

What you want to do is find the profit, subject to there being a positive demand (price<90) which would be

Profit=Revenue per week - Cost per week







Find stationary values by taking the first derivative of the profit function and setting it to 0, remembering the above condition then confirm which of the answers is a maximum by finding which would make the second derivative negative

Ugh, it's late. Okay, so if I take P'(x) I get , correct? Forgive me, but refresh me on how exactly to find the specific stationary values. Also, if I take the derivative, again, of the above profit function it would be ; is that right?

It must be late, you differentiated it incorrectly it's







so the stationary values would be p=90 and p=50

if you plug them into the second differential

you find that its negative for p=50 and positive for p=90

so it's maximised for p=50