A market has the following demand and supply equations:
Qd = -50P + 1000
Qs = 150P - 400
Which of the following statements is true?
a. If the price were $9, a surplus of 300 units would exist and price would tend to fall.
b. If the price were $3, a shortage of 800 units would exist and price would tend to rise.
c. The equilibrium price and quantity, respectively are $8 and 600 units.
d. The equilibrium price and quantity, respectively are $6 and 500 units.
Plug in $9 and $3 for P and see what you get for Qd and Qs.
For the equilibrium proce, set Qd = Qs and solve for P. See if it agrees with c. or d.
I see two correct choices.
To determine which statement is true, we will first calculate the equilibrium price and quantity using the given demand and supply equations.
Equating the demand and supply equations, we have:
-50P + 1000 = 150P - 400
Rearranging and combining like terms:
200P = 1400
Dividing both sides by 200:
P = 7
To find the equilibrium quantity, substitute the equilibrium price (P = 7) into either the demand or supply equation. Using the demand equation:
Qd = -50P + 1000
Qd = -50(7) + 1000
Qd = -350 + 1000
Qd = 650
Therefore, the equilibrium price and quantity are $7 and 650 units, respectively.
Now let's evaluate each statement:
a. If the price were $9, a surplus of 300 units would exist and price would tend to fall.
Substituting P = 9 into the demand equation:
Qd = -50(9) + 1000
Qd = -450 + 1000
Qd = 550
Substituting P = 9 into the supply equation:
Qs = 150(9) - 400
Qs = 1350 - 400
Qs = 950
The quantity demanded (550) is less than the quantity supplied (950), indicating a surplus. Therefore, statement a is false.
b. If the price were $3, a shortage of 800 units would exist and price would tend to rise.
Substituting P = 3 into the demand equation:
Qd = -50(3) + 1000
Qd = -150 + 1000
Qd = 850
Substituting P = 3 into the supply equation:
Qs = 150(3) - 400
Qs = 450 - 400
Qs = 50
The quantity demanded (850) is greater than the quantity supplied (50), indicating a shortage. Therefore, statement b is true.
c. The equilibrium price and quantity, respectively, are $8 and 600 units.
From our earlier calculations, we determined that the equilibrium price and quantity are $7 and 650 units, respectively. Therefore, statement c is false.
d. The equilibrium price and quantity, respectively, are $6 and 500 units.
From our earlier calculations, we determined that the equilibrium price and quantity are $7 and 650 units, respectively. Therefore, statement d is false.
Based on our analysis, the correct statement is b. If the price were $3, a shortage of 800 units would exist and price would tend to rise.