Question

What are the “Dorfman-Steiner” conditions? Could you derive the formula?(Hint: You may need to look online for this answer if it is not covered in class. Write down a revenue function and take derivative.)

Answer 1

Dorfman Steiner condition say that the optimal level of advertisement is the ratio between the elasticity of advertising and elasticity of price. saying in another way, advertisement increases with its own effectiveness but it decreases with price elasticity.

To derive the Dorfman Steiner condition, let us take a profit function as,

π=(p−c)⋅q(p,a)−a

where, p= price, q= quantity sold, a= advertisement made, c= constant marginal cost.

Differentiating the above profit function with respect to price we get,

dπ/dp=q(p,a)+(p−c)∂q/∂p=0 ..................(1)

and differentiating the above profit function with respect to level of advertisement we get,

dπ/da=(p−c)∂q/∂a−1=0 ......................(2)

Let us denote the price elasticity as η≡−(∂q/∂p)(p/q)>0 and the advertisement elasticity as θ≡(∂q/∂a)(a/q)>0

Rewriting equation (1) we get, η=p/p−c ...................(3)

Rewriting equation (2) we get, a/p⋅q= (p−c/p)θ ..................(4)

Combining equations (3) and (4) we get,

a/p⋅q=θ/η

This is the Dorfman Steiner condition.