Answer:
Demand Equation: q = 15125 - 25p.
Supply Equation: 80p - 24000 = 9q.
Equilibrium Price: $525.
Equilibrium Quantity: 2000 units.
Step-by-step explanation:
To solve this question, first, the demand equation has to be calculated. Let price be on the y-axis and quantity by on the x-axis. It is given that p = $485 when q = 3000 units. This can also be written as (q₁, p₁) = (3000, 485). It is also given that when the price goes down by $20, the quantity increases by 500 units. Therefore, (q₂, p₂) = (3500, 465). Due to the statement "For each decrease in unit price of $20 below $485, the quantity demanded increases by 500 units", the demand function will be linear i.e. a straight line. This is because the word "for each" has been used. Therefore, finding the equation of the demand function:
(p - p₁)/(q - q₁) = (q₂ - q₁)/(p₂ - p₁).
(p - 485)/(q - 3000) = (465 - 485)/(3500 - 3000).
(p - 485)/(q - 3000) = (-20)/(500).
(p - 485)/(q - 3000) = -1/25.
25*(p - 485) = -1*(q - 3000).
25p - 12125 = -q + 3000.
25p + q = 15125.
q = 15125 - 25p. (Demand Equation).
Second, find the supply equation. It is given that the suppliers will not sell the product below or at the price of $300. Therefore, (q₁, p₁) = (0, 300). Also, the suppliers will sell 2000 units if the price is $525. Therefore, (q₂, p₂) = (2000, 525). Since it is mentioned that supply equation is linear, therefore:
(p - p₁)/(q - q₁) = (q₂ - q₁)/(p₂ - p₁).
(p - 300)/(q - 0) = (525 - 300)/(2000 - 0).
(p - 300)/(q) = (225)/(2000).
(p - 300)/(q) = 9/80.
80*(p - 300) = 9*(q).
80p - 24000 = 9q. (Supply Equation).
Equilibrium exists when demand = supply. This means that the demand and the supply equations have to be solved simultaneously. Therefore, put demand equation in supply equation:
80p - 24000 = 9(15125 - 25p).
80p - 24000 = 136125 - 225p.
305p = 160125.
p = $525.
Put p = $525 in demand equation:
q = 15125 - 25p.
q = 15125 - 25(525).
q = 15125 - 13125.
q = 2000 units.
To summarize:
Demand Equation: q = 15125 - 25p!!!
Supply Equation: 80p - 24000 = 9q!!!
Equilibrium Price: $525!!!
Equilibrium Quantity: 2000 units!!!
