The equilibrium condition for three related markets is given by:

11 P 1 P 2 P 3 31

P 1 6 P 2 2 P 3 26

P 1 2 P 2 7 P 3 24

Using matrix inverse method, find the equilibrium price for each market.

(b) Assume that two products, Gleem and Sparkle, currently share the market with shares of 60% and

40% each respectively. Each week some brand switching takes place. Of those who bought

Gleem the previous week, 70% buy it again, whilst 30% switch to Sparkle. Of those who bought

Sparkle the previous week, 80% buy it again, whilst 20% switch to Gleem.

Determine the position:

(i)One week from now

(ii)Two weeks from now

(iii)In the long run