Consider a soft (cola) drinks market where two firmsFirm A and Firm Bcompete for market shares given by the multinomial logit (MNL) functions below:

= 0.2 0.2+ , and = 0.2+ ,

where and respectively denote the market shares of Firms A and B when its corresponding products are priced at and ; moreover, price sensitivity parameter for Firm B's customers, i.e, , is unknown to youFirm A's marketing/pricing specialist. However, your past marketing/pricing data suggest that is between 0.2 and 0.8.

a) (2 pts) Use the data set given in the table below to determine the value of

Price of Firm APrice of Firm BMarket Share of Firm AMarket Share of Firm

Price of Firm A Price of Firm B Market Share of Firm A Market Share of Firm B

1 1 0.549833997 0.450166003

2 2 0.59868766 0.40131234

b) (2 pts) As a newly hired marketing/pricing manager of Firm A, your goal is to increase your market share up to 70% when both firms price the product at $2.50. You decide to launch a new marketing/branding campaign to improve the product awareness and brand loyalty of your product, and thereby reduce the value of to increase the market share (). What is the target value of that takes your firms market share to 70%?