Please solve this The management of the Titan Tire Company has determined that t

Question

Please solve this

The management of the Titan Tire Company has determined that the quantity demanded x of their Super Titan tires/week is related to the unit price p by the relation p = 164 - x^2 where p is measured in dollars and x is measured in units of a thousand. Titan will make x units of the tires available in the market if the unit price is p = 68 + 1/2x^2 2 dollars. Determine the consumers' surplus and the producers' surplus when the market unit price is set at the equilibrium price. (Round your answers to the nearest dollar.)

Explanation / Answer

At Equilibrium , Quantity Demanded = Quantity Produced

.

x^2 = 164 - p .... Equation-1

0.5x^2 = -68 + p ....Equation-2

..

Adding Equatiuon 1 & 2 we get,

1.5 x^2 = 96

x^2 = 64

x = 8 units. .....Equilibrium Quantity

therefore , Equilibrium Price (p) = 164 - (8^2)

= 164 - 64

= $100

..

Consumer's Surplus = NIL

Producer's Surplus = Nil

At equilibrium price and Equilibrium Quantity

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