Suppose that the supply function for a certain product is p = S ( x ) = x 2 + 2

Question

Suppose that the supply function for a certain product is

p = S(x) = x2 + 2x + 32 where x 0

And the demand function for this same product is

p = D(x) = 144 x2 where x 0

where p is measured in dollars and x is measured in units of a thousand.

Answer the following questions. Round answers to two decimal digits. Include correct units.

p =

x =

Find the equilibrium quantity and equilibrium price for this product.

Find the consumers' surplus at the equilibrium price.

Find the producerss' surplus at the equilibrium price.

Explanation / Answer

Equilibrium will happen when demand became equal to supply:

x2 + 2x + 32 = 144 x2

2 x2 + 2 x – 112 = 0

x2 + x – 56 = 0

x2 + 8x - 7 x -56 =0

(x+8)(x-7)=0

x =7

Equilibrium quantity is 7000 units

Equilibrium price is, p = 144-(7)2

Equilibrium price is, p = $95

Calculate the area of your triangle using the formula 1/2 x height x base

Maximum price is when x=0 in demand function – p = 144-0 = $ 144 ----height of triangle

Base of triangle is value of x or 7

Area = ½*144*7 = 504

Consumer surplus is $ 504

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