. 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?
i tried to figure out the market demand equation first and I got 80-6p. However when I try to solve for the mkt equilbrium price and q, I get decimals and its not working.
To find the market equilibrium price and quantity, you need to solve for the point where the quantity demanded (QD) is equal to the quantity supplied (QS).
First, set QD,1 equal to QD,2:
20 - P = 60 - 5P
Now, solve for P:
20 + 4P = 60
4P = 40
P = 10
Next, substitute this value of P back into one of the demand equations to find the corresponding market quantity:
QD,1 = 20 - P
QD,1 = 20 - 10
QD,1 = 10
Alternatively, you can also substitute back into the other demand equation to double-check:
QD,2 = 60 - 5P
QD,2 = 60 - 5(10)
QD,2 = 60 - 50
QD,2 = 10
Now, substitute the equilibrium price (P = 10) back into the supply equation to find the equilibrium quantity:
QS = -18 + 3P
QS = -18 + 3(10)
QS = -18 + 30
QS = 12
Therefore, the market equilibrium price is P = 10 and the market equilibrium quantity is Q = 12.