Consider a perfectly competitive market with market supply $Q ^ { s } = - 2 + P$ and market demand $Q ^ { d } = 30 - P$. What is total surplus in this market?
A) 98
B) 128
C) 196
D) 256

Question

Quizplus · Accepted Answer

To find the total surplus in the market, we need to find the equilibrium price and quantity.

Setting the market supply equal to the market demand gives:

$$ -2 + P = 30 - P $$

Solving for P gives:

$$ P = 16 $$

Plugging P back into either the market supply or demand equation gives the equilibrium quantity:

$$ Q = 14 $$

To calculate total surplus, we need to find the area between the demand curve and the supply curve up to the equilibrium quantity.

The area of the triangle bounded by the equilibrium quantity, the y-axis, and the demand curve represents consumer surplus.

The area of the triangle bounded by the equilibrium quantity, the y-axis, and the supply curve represents producer surplus.

The total surplus is the sum of the consumer surplus and producer surplus:

$$ 	ext{Total Surplus} = 	ext{Consumer Surplus} + 	ext{Producer Surplus} $$

$$ 	ext{Total Surplus} = \frac{1}{2}(30-16) 	imes 14 + \frac{1}{2}(16-(-2)) 	imes 14 $$

$$ 	ext{Total Surplus} = 98 + 98 $$

$$ 	ext{Total Surplus} = 196 $$

Therefore, the best choice is C. To find the total surplus in a perfectly competitive market, we need to find the area between the supply and demand curves up to the equilibrium quantity. The equilibrium quantity is found by setting supply equal to demand:

$-2 + P = 30 - P$

$2P = 32$

$P = 16$

$Q = Q^s = Q^d = 14$

We can now calculate the total surplus:

$CS = \frac{1}{2}(P_E - 0)(Q^d - Q^s) = \frac{1}{2}(16 - 0)(30 - 14) = 128$

$PS = \frac{1}{2}(16 - 0)(14 - (-2)) = 144$

$TS = CS+ PS = 128 + 144 = 272$

Therefore, the total surplus in this market is $272$. Only choice C matches this value, so the answer is C.

Consider a Perfectly Competitive Market with Market Supply Qs=−2+PQ ^ { s } = - 2 + PQs=−2+P

Consider a Perfectly Competitive Market with Market Supply $Q ^ { s } = - 2 + P$