Question

Consider a perfectly competitive market where the demand for the good is given by Q=894-20p, where Q denotes the quantity demanded at price p. On the supply side, the industry supply function is given by Q=-6+6p. Find the equilibrium price, p*, and quantity, Q*, in this market. Then enter below the value of Q*, i.e., the value of the equilibrium quantity.

Answer 1

The equilibrium price in the perfectly competitive market is approximately $34.62, and the equilibrium quantity is approximately 207 units.

Step-by-step explanation:

To find the equilibrium price and quantity in a perfectly competitive market, we can set the quantity demanded (Qd) equal to the quantity supplied (Qs). The demand function is given as Q = 894 - 20p and the supply function is Q = -6 + 6p.

Setting Qd equal to Qs:

894 - 20p = -6 + 6p

Adding 20p to both sides and adding 6 to both sides we get:

900 = 26p

Dividing both sides by 26 to solve for p we find:

p* = 900 / 26 ≈ 34.62

Now we substitute p* back into either the demand or supply equation to find the equilibrium quantity, Q*:

Q* = -6 + 6p* = -6 + 6(34.62) = 207.72

Thus, the equilibrium price, p*, is approximately $34.62 and the equilibrium quantity, Q*, is approximately 207 units.