Question

Suppose that the demand per ounce of a rare type of chocolate, Q

​ , is represented by the following equation, where P is the price of chocolate and Q
is the quantity of chocolate sold:
Q = 2200 − 18P
The supply of chocolate, Qs. is represented by the equation:
Qs = −500 + 81P
Find the equilibrium price and quantity of chocolate sold. Give your answers to two decimals.

Answer 1

The equilibrium price is $27.27 and the equilibrium quantity is 1708.54 ounces of chocolate sold.

Step-by-step explanation:

To find the equilibrium price and quantity of chocolate sold, we need to set the demand and supply equations equal to each other.

Q = 2200 - 18P

Qs = -500 + 81P

Setting Q and Qs equal to each other:

2200 - 18P = -500 + 81P

99P = 2700

P = 27.27 (rounded to two decimals)

Using the equilibrium price, we can find the equilibrium quantity by substituting P into either the demand or supply equation:

Q = 2200 - 18P

Q = 2200 - 18(27.27)

Q = 2200 - 491.46

Q = 1708.54 (rounded to two decimals)

The equilibrium price is $27.27 and the equilibrium quantity is 1708.54 ounces of chocolate sold.