Question

1. Suppose the market demand is described as P = 15 - Qd: , while the market supply function is: P = 3 + Qs/11. Suppose the current market is at equilibrium. What is the producer surplus? (Hint: You need to calculate market equilibrium price and equilibrium quantity.)  

		11
		8
		6
		5.5

What is the total surplus?

		44
		60.5
		66
		72.5

Answer 1

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