Consider a perfectly competitive market with inverse market supply $P = 5 + 3 Q ^ { s }$ and inverse market demand $P = 50 - 2 Q ^ { d }$ . Suppose the government subsidizes this market with a subsidy of $5 per unit. What are the equilibrium price and quantity traded before the subsidy?
A) P = 30; Q = 10
B) P = 25; Q = 12.5
C) P = 32; Q = 9
D) P = 35; Q = 7.5

Question

Quizplus · Accepted Answer

To find the equilibrium price and quantity traded before the subsidy, we need to set the market supply and demand functions equal to each other:

$5 + 3Q^s = 50 - 2Q^d$

Solving for Q, we get:

$Q = \frac{45}{5 + 5Q^s}$

Substitute this expression into either the supply or demand equation to solve for P:

$P = 5 + 3Q^s = 5 + 3\left(\frac{45}{5 + 5Q^s}\right) = 32$

So the equilibrium price before the subsidy is $32. To find the equilibrium quantity, we can substitute this price back into either the supply or demand equation and solve for Q:

$Q = \frac{50 - P}{2} = \frac{50 - 32}{2} = 9$

So the equilibrium quantity before the subsidy is 9 units. Therefore, the correct answer is C.

Consider a Perfectly Competitive Market with Inverse Market Supply P=5+3QsP = 5 + 3 Q ^ { s }P=5+3Qs

Consider a Perfectly Competitive Market with Inverse Market Supply $P = 5 + 3 Q ^ { s }$