Suppose that the demand and supply for artificial Christmas trees is given by th

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 = 107.10-0.30q (demand function) p = 0.01 q2 + 5.31 (supply function) Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. The equilibrium price of $ gives a demand that is equal to a supply of hundred trees. (Simplify your answer. Type integers or simplified fractions.) The equilibrium price does not exist.

Explanation / Answer

p = 107.10 - 0.30q

and p = 0.01q^2 + 5.31

Then 0.01q^2 + 5.31 = 107.10 - 0.30q

0.01q^2 + 0.30q - 101.79 = 0

q = 87 (q = -117 is not possible)

Then p = 107.10 - 0.3*87 = 81

So, price = p = $81

Quantity of trees = q = 8700

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