The GT brewery has hired you as an analyst to understand its market position. It is particularly concerned about its major compe
titor, the ML Brewery, and which brewery has the ‘lead’ market share. Recent history has suggested that which brewery has the ‘lead market share’ can be modeled as a Markov Chain using three states: GT, ML, and Other Company (OC). Data on the lead market share is taken monthly and you have constructed the following one-step transition probability matrix from past data:
GT ML OC
GT 0.75 0.15 0.10
ML 0.30 0.60 0.10
OC 0.20 0.10 0.70
a. The current state of the lead market share in November is GT·The GT Brewery is considering launching a new brand in March only if it has the lead market share in February. Determine the probability that GT Brewery will launch this new brand. Please show any equations or matrices used to calculate this probability and briefly explain how you obtained your answer.
b. Provide the steady-state equations and calculate the steady-state probabilities for the Markov Chain.
GT ML OC
GT 0.75 0.15 0.10
ML 0.30 0.60 0.10
OC 0.20 0.10 0.70
a. The current state of the lead market share in November is GT·The GT Brewery is considering launching a new brand in March only if it has the lead market share in February. Determine the probability that GT Brewery will launch this new brand. Please show any equations or matrices used to calculate this probability and briefly explain how you obtained your answer.
b. Provide the steady-state equations and calculate the steady-state probabilities for the Markov Chain.
1 answer:
You might be interested in
Answer:
12.0 tablet computers/month
Step-by-step explanation:
The average price of the tablet 25 months from now will be:
Next, we determine the rate at which the quantity demanded changes with respect to time.
Using Chain Rule (and a calculator)
Therefore:
Recall that at t=25,
Therefore:
The quantity demanded per month of the tablet computers will be changing at a rate of 12 tablet computers/month correct to 1 decimal place.