Question

Take a total cost function, equal to C(y) = 50 + 0.5*y^2. Suppose there are 10 firms, all with that same cost function, in a market whose aggregate demand is given by Y=150-p. a) Compute each firm’s supply, aggregate (total) supply and the competitive equilibrium. b) Compute the elasticity of demand to price, at equilibrium.

Answer 1

a)

TC = 50+0.5Y^2

MC = delta TC / delta Y

MC = Y

For a competitive firm, P = MC at equilibrium

So, P = Y

Y = P is the individual firm supply equation

Since, there are 10 firms

So, Aggregate Supply:

Y = 10P

Aggregate Demand: Y=150- P

P = 150 - Y ----------equation 1

at competitive equilibrium, P = MC

150 - Y = Y using equation 1

Y = 75

P = 150 - 75 = 75

b)

at P = Y = 75

Elasticity of Demand = (deltaY / deltaP) * (P/Y)

Elasticity of Demand = - 1 * (75/75) using the aggregate demand equation

Elasticity of Demand = - 1

So, it has unitary elastic demand.