The demand for x camcorder tapes, in thousands, is given by: p = -.01 x^2 - .2x

Question

The demand for x camcorder tapes, in thousands, is given by: p = -.01 x^2 - .2x + 23. Determine Consumer's Surplus at the price-demand level p- = $8. The number x of DVD players a supplier is willing to make available is given by: p = .0003x^2 + .1x + 10. Determine the Producer's Surplus at the price-supply level p- = $67. The quantity demanded x, in hundreds, of 5 Times 7 tents/week is related by p = -.1x^2 - x + 40. The quantity in hundreds, that a supplier is willing to make available is related by p = .1 x^2 + 2x + 20. Find the equilibrium quantity and price. Find the Consumer Surplus. Find the Producer Surplus.

Explanation / Answer

First we find the equilibrium price and quantity by equation the demand and supply functions

-0.1x^2 - x + 40 = 0.1x^2 + 2x + 20

0.2x^2 + 3x - 20 = 0

On solving this, we get x = {-20, 5}, so x = 5

p = 0.1(5^2) + 2(5) + 20 = 32.5

Producer's surplus = Area under the price curve but above the supply curve

= (32.5 - (0.1x^2 + 2x + 20))dx over [0, 5]

= (12.5 - 0.1x^2 - 2x)dx over [0, 5]

= 12.5x - (0.1/3)x^3 - x^2 over [0, 5]

= 12.5(5) - (0.1/3)(5^3) - 5^2 = 33.33

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