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 March 15th, 2012, 02:51 PM #1 Senior Member   Joined: Feb 2012 Posts: 110 Thanks: 0 marginal price and price-demand This is a word problem. I really don't understand what they are asking here. If the marginal price dp/dx at x units of demand per week is proportional to the price p, and if at $80 there is no weekly demand [p(0)=80] and if at$50.18 there is a weekly demand of 8 units [p(=50.18] find the price-demand equation Thank you for your help. I really appreciate it. This site helps so much. Thank you for everyone that has helped me in the past.
 March 15th, 2012, 03:01 PM #2 Senior Member   Joined: Feb 2012 Posts: 628 Thanks: 1 Re: marginal price and price-demand $\frac{dp}{dx}= kp$ $\frac{dp}{p}= k dx$ $\ln p= kx + C$ $p= Ae^{kx}$ $80= Ae^{k \cdot 0} = Ae^0 = A$ $50.18= 80e^{8k}$ $\frac{50.18}{80}= e^{8k}$ $\ln \left(\frac{50.18}{80}\right)= 8k$ $k= \frac{1}{8} \ln \left(\frac{50.18}{80}\right)$ so the price-demand equation is $p= 80e^{kx}$ where k is calculated as above.
 March 15th, 2012, 03:07 PM #3 Senior Member   Joined: Feb 2012 Posts: 110 Thanks: 0 Re: marginal price and price-demand thank you iceman. That cleared things up completely.

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### the marginal price dp/dx at x units of demand per week is proportional

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