Question

Suppose that the demand and supply functions for good X are
Qd = 50 - 8P and Qs = -17.5 + lOP
a. What are the equilibrium price and quantity?
b. What is the market outcome if price is $2.75? What do you expect to happen? Why?
c. What is the market outcome if price is $65.25? What do you expect to happen? Why?
d. What happens to equilibrium price and quantity if the demand function becomes Qd = 59 - 8P?

Answer 1

Question with solutions:

a) Suppose that the demand and supply functions for good X are $Qd = 50 - 8P$ and $Qs = -17.5 + IOP$ a. What are the equilibrium price and quantity?

a) The equilibrium is in the point, where $Qd = Qs$ So, we put the equations of the demand and supply into the equality.

$$50 - 8P = -17.5 + 10P$$ $$18P = 67.5$$

$P = \$3.75$ is equilibrium price.

$Q = 50 - 8*3.75 = 20$ units is equilibrium quantity.

b) What is the market outcome if price is \$2.75? What do you expect to happen? Why?

For the lower price the quantity demanded will rise and the quantity supplied will fall, so there will be a shortage of product on the market.

c) What is the market outcome if price is \$65.25? What do you expect to happen? Why?

For the much more higher price the quantity demanded will fall sharply and the quantity supplied will rise sharply, so there will be a great surplus of the product on the market.

d) What happens to equilibrium price and quantity if the demand function becomes $Qd = 59 - 8P$?

Let us repeat the steps from the question 1.

$$Qd = Qs$$ $$59 - 8P = -17.5 + 10P$$ $$18P = 78.5$$

$P = \$4.36$, $Q = 24$ units are new equilibrium price and quantity.