Question

# The demand for a product is Qd=320-8p-2px and supply is Qs=20+4p, where Q is the quantity...

The demand for a product is Qd=320-8p-2px and supply is Qs=20+4p, where Q is the quantity for the product, in thousands of units, P is the price of the product, and Px is the price of the another good X

1) When Px =\$30, what is the equilibrium price and quantity sold for the product?

2) At the equilibrium price and quantity, what is the price elasticity of demand for the product?

1)

Equilibrium in the market occurs when Quantity demand = quantity supplied.

Here it is given that Demand is Qd=320-8p-2px and supply is Qs=20+4p also px = 30

Hence Qd = 260-8p and Qs =20+4p

Hence At equilibrium, 260-8p =20+4p

=> p = 20 -------------Equilibrium price

Hence Q = 20 + 4*20= 100 -------------------Equilibrium Quantity

2)

Price elasticity of demand = (dQd/dp)(p/Qd)

As, Qd = 260-8p => dQd/dp = -8 and as calculated above at equilibrium price(p) = 20 and Q = 100

Hence, Price elasticity of demand = -8(20/100) = -1.6

=> Price elasticity of demand = (-)1.6

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