Question

a certain product has supply and demand functions given by $p = 60q + 300$ and $p = 5300 - 40q$, respectively. (a) if the price $p$ is $\\$2100$, how many units $q$ are supplied and how many are demanded? (b) what price gives market equilibrium, and how many units are demanded and supplied at this price? (a) when the price $p$ is $\\$2100$, there are $\square$ units supplied and $\square$ units demanded. (simplify your answer.)

Explanation:

Step1: Solve for supplied q (p=2100)

Substitute $p=2100$ into $p=60q+300$:
$$2100 = 60q + 300$$
$$60q = 2100 - 300$$
$$60q = 1800$$
$$q = \frac{1800}{60} = 30$$

Step2: Solve for demanded q (p=2100)

Substitute $p=2100$ into $p=5300-40q$:
$$2100 = 5300 - 40q$$
$$40q = 5300 - 2100$$
$$40q = 3200$$
$$q = \frac{3200}{40} = 80$$

Step3: Find equilibrium (set p equal)

Set $60q + 300 = 5300 - 40q$:
$$60q + 40q = 5300 - 300$$
$$100q = 5000$$
$$q = \frac{5000}{100} = 50$$

Step4: Find equilibrium price

Substitute $q=50$ into $p=60q+300$:
$$p = 60(50) + 300 = 3000 + 300 = 3300$$

Answer:

(a) When the price p is $2100, there are 30 units supplied and 80 units demanded.
(b) The market equilibrium price is $3300, with 50 units supplied and demanded.