Find Equilibrium quantity and price.
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The quantity of watches demanded per month is related to the unit price by the equation:
p = d(x) = 50/ (0.01x^2 + 1) (1 less than equal x less than equal 20)
where p is measured in dollars and x is measured in units of a thousand. The supplier is willing to make x thousand watches available per month when the price is given by p =s(x) = 0.1x + 20 dollars.
Find the equilibrium quantity and price.
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Solution Summary
This solution shows all the steps for calculating the equilibrium quantity and price in the given problem.
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At equilibrium, demand = supply
50/(0.01x^2 + 1) = 0.1x + 20
50 = (0.01x^2 + 1)(0.1x + 20) = 0.001x^3 + 0.20x^2 + 0.1x + 20
0.001x^3 + 0.20x^2 + 0.1x - 30 = 0
We solve for x using Newton-Raphson Method
f(x) = 0.001x^3 + ...
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