another demand function

johnjones

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Sep 8, 2005
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Demand (sales) for a certain type of toy is found to be D(p) = 400 - 60p toys per week at the unit price $p. At this price, suppliers are willing to produce S(p) = 10p^2 toys per week.

Find dR/dp at the equilibrium price.

I'm not sure if I'm doing it right, but I set D(p)=S(p), to get one function.
p^2 + 6p - 40, then I took the derivative of that, to get.

2p + 6.

Or do I use R = xp to get a revenue function?
R = x(demand functioin)
= x(400 - 60p)

But the problem is that I have both x and p... then how is the revenue function going to work? For a demand function... isn't x usually the quantity, not p?
:shock:
 
The revenue function is R(p)=pD(p)=400p-60p<SUP>2</SUP>.
The equilibrium price: 400-60p=10p<SUP>2</SUP> or when p=4.
Now find R’(4).
 
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