Question

Suppose that the demand and supply for artificial Christmas trees is given by the functions below where p is the price of a tree in dollars and q is the quantity of trees that are demanded/supplied in hundreds. Find the price that gives the market equilibrium price and the number of trees that will be sold/bought at this price.p=109.70−0.10q (demand function)p=0.01q2+5.91 (supply function)

Answer 1

The equilibrium price is the price at which the demand function is equal to the supply function.

Hence it is given by:

$\begin{gathered} 109.70-0.10q=0.01q^2+5.91 \\ 0.01q^2+0.10q-103.79=0 \end{gathered}$

Solve the quadratic equation to get:

q=97,-107.

Now the quantity cannot be negative hence the value of q=97. Hence 97 hundred trees is the demand.

The equilibrium price is given by:

$p=109.70-0.10q=100\text{ dollars}$

Hence Option A is correct and the boxes to be filled is given by the statement given below:

The equilibrium price of $100 gives a demand that is equal to a supply of 97 hundred trees.