assume that the demand and supplu equations for bushels of wheat are as follows
Qd=15-(3*P)
Qs=1+(4*P)
Also assume that, the equilibrium, Qd=Qs solve for equilibrium price by setting quanity demand equal to quanity supplied. what is the disequilibrim condition at prices of $150. $2.50.
I am having problems with this problem, please help
thank you
set 15-3P=1+4P. Solve for P (using algebra).
Plug in 1.5 for P in the supply and demand equations, What is Qd, what is Qs. Is there a surplus or shortage (hint: a shortage as quantity demanded exceeds quantity supplied). Repeat with 2.5 for P.
To solve for the equilibrium price, set the quantity demanded equal to the quantity supplied:
Qd = Qs
Substituting the given equations for Qd and Qs, we have:
15 - 3P = 1 + 4P
To solve for P, we need to isolate the variable by manipulating the equation. Let's start by collecting like terms:
15 - 1 = 4P + 3P
14 = 7P
Next, divide both sides of the equation by 7:
P = 2
Therefore, the equilibrium price is $2.
To determine the disequilibrium condition at prices of $150 and $2.50, we need to substitute these prices into the supply and demand equations and compare the quantities demanded and supplied.
At a price of $150:
Qd = 15 - (3 * 150)
Qd = 15 - 450
Qd = -435
Qs = 1 + (4 * 150)
Qs = 1 + 600
Qs = 601
As we can see, the quantity demanded (Qd) is negative, indicating an unfeasible condition. On the other hand, the quantity supplied (Qs) is positive, indicating a surplus.
At a price of $2.50:
Qd = 15 - (3 * 2.50)
Qd = 15 - 7.50
Qd = 7.50
Qs = 1 + (4 * 2.50)
Qs = 1 + 10
Qs = 11
In this case, the quantity demanded (Qd) is 7.50, and the quantity supplied (Qs) is 11. The quantity demanded is lower than the quantity supplied, indicating a shortage.
Therefore, at a price of $150, there is a surplus, and at a price of $2.50, there is a shortage.