Question

The supply curve for pianos is given by the following: Qs = p-6000. Further, the demand curve for pianos is given by Qd = 18000 – 2p. Let e_d be the own price elasticity of demand and e_s the own price elasticity of supply. In the market equilibrium for pianos:

Group of answer choices

e_d is elastic and e_s is inelastic

e_d is inelastic and e_s is elastic

e_d is elastic and e_s is elastic

e_d is inelastic and e_s is inelastic

Answer 1

Market equilibrium happens when Qd = Qs

So, 18000 – 2p = p-6000

On solving p = 8000

Putting this in Qd or Qs gives quantity to be 2000

So the equilibrium price is 8000 and the equilibrium quantity is 2000

Ed = dQ/dP * P/Q = (1/ Slope of demand curve) * (P/Q)

the slope of given demand curve is -2

So, Ed = - (1/2) * (8000/2000) = - 2

Now, Es = dQ/dP * P/Q = (1/ Slope of supply curve) * (P/Q)

the slope of given supply curve is 1

So, Ed = (1/1) * (8000/2000) = 4

Since the absolute values of both Ed and Es are greater than 1. Therefore, both Ed and Es are elastic at the equilibrium with Es being relatively more elastic as its value is greater than Ed.

Hence the correct option is c) Ed is elastic and Es is elastic

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