11 |
||
8 |
||
6 |
||
5.5 |
What is the total surplus?
44 |
||
60.5 |
||
66 |
||
72.5 |
Answer:
Producer surplus = 5.5
Total surplus = 66
Calculation:
In order to find equilibrium price and quantity, we must equate demand and supply functions.
15 - Q = 3 + Q/ 11
15 - 3 = Q/11 + Q
12 = 12/ 11 Q
Q = 12 * 11/ 12 = 11 Q = 11
P = (15 - 11) = 4 OR P = (3 + 11 / 11) = 4 P = 4
(plugging in value of Q in demand function OR supply function)
Producer surplus(PS) is calculated as the area of the triangle above the supply curve and below the equilibrium price line. We need to find Y intercept. i.e. supply curve will touch y-axis when Q = 0, and P = 3(supply function --- P = 3 + Q/ 11). -----(i)
So PS will be
PS = ½ * (4 - 3) * 11 = ½ * 1 * 11 = 5.5 PS = 5.5
Total surplus is the area of the triangle formed by three points: y intercept by demand curve, y intercept by supply curve and equilibrium point where P = 4 and Q = 11.
Y intercept by demand curve (upper intercept) will be when Q = 0 in the demand function (P = 15 - Q) That will be when price = 15. (15 = 15 - 0)
Y intercept by supply curve (lower intercept) will be when Q = 0 in the supply function, that is when Price = 3------ [ from (i) above]
Total surplus = ½ * (upper intercept on y-axis - lower intercept on y-axis) * quantity
= ½ (15 - 3) * 11 = ½ * 12 * 11 = 66
Total surplus = 66
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