Question 1199379: The demand and supply functions are given by:
P=100-2Qd, and P=20+2Qs respectively, where P, Qd, and Qs represent the prices, quantities demanded, and quantities supplied.
(Prices are measured in € and Quantities in Units)
i. Find the equilibrium point algebraically and graphically.
ii. Calculate and explain consumer surplus, producer surplus and total surplus.
Answer by ikleyn(52814) (Show Source):
You can put this solution on YOUR website! .
The demand and supply functions are given by:
P=100-2Qd, and P=20+2Qs respectively, where P, Qd, and Qs represent the prices, quantities demanded, and quantities supplied.
(Prices are measured in € and Quantities in Units)
(a) Find the equilibrium point algebraically and graphically.
(b) Calculate and explain consumer surplus, producer surplus and total surplus.
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In the equilibrium point, the values Qd and Qs are the same, Qd = Qs,
So we replace them by single variable Q in equations.
We get then two equations in two unknowns
P = 100 - 2Q, (1)
P = 20 + 2Q. (2)
In these equations, left side is the same, so right side must be equal
100 - 2Q = 20 + 2Q,
or
100 - 20 = 2Q + 2Q,
80 = 4Q
Q = 80/4 = 20.
Then from equation (1)
P = 100 - 2*20 = 100 - 40 = 60.
ANSWER. The equilibrium point is (P,Q) = (60,20).
Part (a) is solved.
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