Suppose demand and supply functions are given by:
2
1
4
1
2
1
7 x
s
x x
d
x Q P and Q P
a. Determine equilibrium P and Q in this market b. Use graph to show market equilibrium
To determine the equilibrium in this market, we need to find the values of price (P) and quantity (Q) at which the demand and supply functions are equal.
a. To find the equilibrium price and quantity, we set the demand and supply functions equal to each other:
Qd = Qs
7 - 2P = -x + 4P - x
To simplify, let's combine like terms:
7 = 5P
Now, solve for P by dividing both sides by 5:
P = 7/5
Substitute this value of P back into either the demand or supply equation to find the equilibrium quantity (Q):
Qd = 7 - 2P
Qd = 7 - 2(7/5)
Qd = 7 - 14/5
Qd = 35/5 - 14/5
Qd = 21/5
Therefore, at the equilibrium point, the price (P) is 7/5 and the quantity (Q) is 21/5.
b. To graphically represent the market equilibrium, we can plot the demand and supply functions on a graph. The x-axis will represent quantity (Q) and the y-axis will represent price (P).
Start by drawing two intersecting lines. One line represents the demand function (Qd = 7 - 2P) and the other line represents the supply function (Qs = -x + 4P - x).
On the y-axis, mark the equilibrium price (P = 7/5) and draw a horizontal line to intersect with the demand and supply lines.
On the x-axis, mark the equilibrium quantity (Q = 21/5) and draw a vertical line to intersect with the demand and supply lines.
The point where these lines intersect represents the market equilibrium.