SOLUTION: 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. (Price

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(52817) (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.
~~~~~~~~~~~~~~~~~~

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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