Question

Refer to the following formula for expected payoff:

Expected payoff= (Probability Of rival matching x Loss from price cut) + (Probability Of rival not matching x Gain from price cut)
Suppose the payoff for each Of four strategic interactions is as follows:

Rival Response
Your Company Action Reduce price Don't Reduce price
Reduce Price Loss=$800 Gain= $50,000
Don't Reduce Price Loss=$6000 No loss or gain

Required:
a. If the probability of rivals matching a price reduction is 98 percent, what is the expected payoff of a price cut?
b. If the probability of rivals reducing price even though you don't is 5 percent, what is the expected payoff Of not reducing price?
b. If the probability of rivals reducing price even though you don't is 5 percent, what is the expected payoff of not reducing price?
c. Based on your answers to (a) and (b), should the firm Cut its price?

Can't determine from the information given
Yes
No

Answer 1

Explanation:

From the given information:

The price reduction = 98% = 0.98

`Then \ the \ expected \ payoff \ = \[(probability \ of \ matching \ price \ reduction \ * \ size \ of \ loss \ from \ price \ cuts \ ) \ + \ ( \ probability \ o f \ rivals\ not \ matching \ * \ gain \ from \ price \ cuts )]`

where;

P(rival not matching ) = (100 - 98)% = 2%

P(rival not matching ) = 0.02

The expected payoff = [(0.98 * -800) + (0.02*50000)]

The expected payoff = [( -784+ 1000)]

The expected payoff = 216

(b) Probability of rivals reducing price = 5%

= 5/100

= 0.05

∴

Probability of rivals reducing price = 1 - 0.05 = 0.95

The expected payoff = (0.05 * -6000) + (0.95 *0)

The expected payoff = -300 + 0

The expected payoff = -300

(c) Yes.

Based on answers (a) and (b), the firm should cut the price.