For a certain product, the demand function is 𝐷(𝑄) = 1000 − 25𝑄 and thesupply function is 𝑆(𝑄) = 100 + 𝑄2. Calculate:a) The market equilibrium price and quantityb) Compute the consumer and producer surplus.

a) The market equilibrium price and quantity are found where the demand function equals the supply function. So, we set 𝐷(𝑄) = 𝑆(𝑄) and solve for 𝑄:

1000 - 25Q = 100 + Q^2

Rearranging terms gives:

Q^2 + 25Q - 900 = 0

This is a quadratic equation in the form ax^2 + bx + c = 0. We can solve for Q using the quadratic formula Q = [-b ± sqrt(b^2 - 4ac)] / (2a):

Q = [-25 ± sqrt((25)^2 - 41(-900))] / (2*1) Q = [-25 ± sqrt(625 + 3600)] / 2 Q = [-25 ± sqrt(4225)] / 2 Q = [-25 ± 65] / 2

This gives two solutions: Q = 20 and Q = -40. Since quantity cannot be negative, we discard Q = -40. So, the equilibrium quantity Q = 20.

Substitute Q = 20 into either the demand or supply function to find the equilibrium price. Using the demand function:

D(20) = 1000 - 25*20 = 500

So, the equilibrium price is 500.

b) Consumer surplus is the area between the demand curve and the price level, up to the quantity sold. It is given by the formula (1/2)baseheight for a triangle. The base is the quantity sold (Q = 20), and the height is the difference between the maximum price consumers are willing to pay (the intercept of the demand function, 1000) and the price they actually pay (500):

Consumer surplus = (1/2)20(1000 - 500) = 5000

Producer surplus is the area between the price level and the supply curve, up to the quantity sold. The base is again the quantity sold (Q = 20), and the height is the difference between the price producers receive (500) and the minimum price they are willing to accept (the intercept of the supply function, 100):

Producer surplus = (1/2)20(500 - 100) = 4000