Question

The quantity demanded x (in units of a hundred) of the Mikado miniature cameras/week is related to the unit price p (in dollars) by p = −0.2x^2 + 220 and the quantity x (in units of a hundred) that the supplier is willing to make available in the market is related to the unit price p (in dollars) by p = 0.1x^2 + 8x + 110 If the market price is set at the equilibrium price, find the consumers' surplus and the producers' surplus. (Round your answers to the nearest dollar.)

Answer 1

We are given

Demand equation:

Supply equation:

We can set them equal

and solve for x

now, we can find price

Consumer Surplus:

we can use formula

now, we can solve it

.........Answer

Producer Surplus:

we can use formula

now, we can set up integral

now, we can solve it

...........Answer