Titorial 3

Question 1

4 sales response models

Answer 1

Linear model
Multiplicative model and semi logarithmic model
Modified exponential mode
S shaped model

Question 2

Determine both the price elasticity and the advertising elasticity according to the above function for an advertising budget of 300€ and a price of 4.30€

Q=2000 +0.7A -350 P
Q = sales
A = advertising
P = price

Answer 2

Price elasticity:

Ep = AQ/AP * P/Q = -350 + 430/(2000+0.7300-3504.3)
=-350*4.3/705 =-2.135

Advertising elasticity

Ea = AQ/AA * A/Q = 0.7A/Q
= 0.7 300/(2000+0.7300-3504.3)

= 0.298

Question 3

Calc the advertising elasticity and price elasticity for a price set equal to 2€ and an advertising budget equal up to 2000€

Q= 1600*P^2 * A^0.5
Q = k * Pa * Ab

Answer 3

AQ/AA * A/Q =4.472 *2000/17888 = B=0.5

Q=1600*2^-2 * 2000^0.5 =17888
AQ/AA = k * pa * b * a ^b-1 = B/A * Q

0.5/2000 * 17888 = 4.472

Question 4

Use an optimality condition to check whether the advertising budget of 2000€ with a price of 2€ and marginal unit cost of 1€ is optimal or not. If not,should advertising budget be increased or decreased?

Q= 1600*P^2 * A^0.5
Q = k * Pa * Ab

Answer 4

Number of units sold:

Q= k * Pa * Ab > Q = 1600 * P^-2 * A^0.5

Costs:

C(Q) = Cvar * Q + Cfix + A

Optimality condition of profit function:
Profit function:
I= P* W - C(Q) > u = (P-Cvar) * k * P^a * Ab - Cfix - A

Optimality condition:
Au/AA = 0.5(2-1) 16002^-2*2000^0.5-1 -1=/ 0
Optimality condition is not fulfilled

Question 5

Q= 1600*P^2 * A^0.5
Q = k * Pa * Ab

Calculate the optimal budget

Answer 5

A optimal = B * (P-Cvar) * Q

0.5(2-1)16002^-2A^0.5 =200 * A^0.5
=40,000

Advertising budget should be increased
Optimal advertising budget is 40,000