Question

Consider a competitive industry with n identical firms each with marginal cost given by MC=8+8q and average variable costs given by AVC=8+4q where q is firm output. Market demand is given by QD (P)=112-P.

(i)Calculate the equilibrium price as a function of n: P(n)

(ii) What is the price and the numerical value of the residual demand elasticity when n=5?

(iii) What is the price elasticity of demand for the market? Why is the residual firm demand’s elasticity so much larger in absolute value?

Answer 1

P= MC = ATC

MC = 8 + 8q

=> Total cost = 8q + 4q²

=> ATC = 8 + 4q

At equilibrium, P = 8 + 8q

Q = nq

So, P = 8 + 8(Q/n)

P = 8 + 8 (112 - P)/n

=> P(1 + 8/n) = 8 + 896/n

=> P = (8 + 896/n)/(1 + 8/n)

ii) Put n = 5, we get P = 72

ε_firm = nε - n₀(n-1) = residual demand elasticity

ε = price elasticity of demand

= dQ/dp × (P/Q)

When n=5, P = 72 => Q = 40

So ε = -72/40 = 1.8

n0 is the supply elasticity. As we aren't given the supply curve it's not possible to calculate.

iii)

The residual demand elasticity is usually having a higher absolute value because a the reaction to prices of other firms are greater than compared to one particular firm due to the competitive nature of the market. More price reaction implies larger change in demand for a small price thereby has a higher absolute value.

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