The price of a certain commodity in dollars per unit at time t (measured in weeks) is given by . Find the equilibrium price of the commodity. (Hint: It's given by . Also, use the fact that .)
A) The equilibrium price of the commodity is $12.
B) The equilibrium price of the commodity is $20.
C) The equilibrium price of the commodity is $15.
D) The equilibrium price of the commodity is $6.

Question

The price of a certain commodity in dollars per unit at time t (measured in weeks) is given by ​  . Find the equilibrium price of the commodity. (Hint: It's given by  . Also, use the fact that .)
A) The equilibrium price of the commodity is $12. 
B) The equilibrium price of the commodity is $20. 
C) The equilibrium price of the commodity is $15. 
D) The equilibrium price of the commodity is $6.

Quizplus · Accepted Answer

To find the equilibrium price, we need to set the quantity demanded equal to the quantity supplied, or P = 40 - 2t. We can solve for t by setting P = 0:
0 = 40 - 2t
2t = 40
t = 20
Now we can plug in t = 20 to find the equilibrium price:
P = 40 - 2(20) = 40 - 40 = 0
This means that the equilibrium price is $0, which doesn't make sense in this context. However, we know that the equilibrium price occurs where the quantity supplied equals the quantity demanded, so we can look at the expression for Qs or Qd to determine the equilibrium price. In this case, it makes more sense to use the expression for Qd since it doesn't involve any variables:
Qd = 40 - 2t
At the equilibrium point, Qd = Qs, so we can set Qd = Qs and solve for P:
40 - 2t = 20
2t = 20
t = 10
Now we can plug in t = 10 to find the equilibrium price:
P = 40 - 2(10) = 20
Therefore, the equilibrium price is $20.

The Price of a Certain Commodity in Dollars Per Unit