Question

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?

Answer #1

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 Q_{d} = 260-8p and Q_{s} =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 = (dQ_{d}/dp)(p/Q_{d})

As, Qd = 260-8p => dQ_{d}/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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