9. Suppose that the total market demand for a product consists of the demands of
individual 1 and individual 2. The demand equations of the two individuals are given by
the following equations:
QD,1 =20-P
QD,2 =60-5P
Suppose that the total market supply is given by the equation:
QS =-18+3P
a. What are the market equilibrium price and quantity? (10 points)
b. Please diagram your answers to part a. (10 point
Im confused because I got 80-6p for my mkt demand but if I make qd=qs im getting decimal answers for p and that doesnt make sense. I know Im doing something wrong but i have no idea what it is.
To find the market equilibrium price and quantity, you need to set the market demand equal to the market supply and solve for the price (P) and quantity (Q). Let's go through the steps to solve this:
a. Setting market demand equal to market supply:
Since the market demand is the sum of the demands of individual 1 and individual 2, we can write it as:
QD = QD,1 + QD,2
Substituting the given demand equations:
QD = (20 - P) + (60 - 5P)
Now, set this market demand equal to the market supply (QS):
QD = QS
Substituting the given supply equation:
(20 - P) + (60 - 5P) = -18 + 3P
Simplify the equation:
20 - P + 60 - 5P = -18 + 3P
Combine like terms:
80 - 6P = -18 + 3P
Add 6P to both sides:
80 = -18 + 9P
Add 18 to both sides:
98 = 9P
Now, divide both sides by 9:
P = 98/9
Calculating the value of P, we get:
P ≈ 10.89
b. Now, to find the market equilibrium quantity (Q), substitute the value of P back into either the supply or demand equation. Let's use the supply equation:
QS = -18 + 3P
Substituting P = 10.89:
QS = -18 + 3(10.89)
Calculate the value:
QS ≈ 11.67
Therefore, the market equilibrium price is approximately 10.89 and the quantity is approximately 11.67.
To diagram your answers, you can create a graph with the price on the vertical axis and quantity on the horizontal axis. Plot the market demand curve and market supply curve, and the point where they intersect will represent the equilibrium price and quantity.