Assume you are managing the company producing 2 different goods, for certainly, x and y. The company sells the product x and y in two local markets, for certainty, denoted as market A and market B. Marketing research segmented the customer population into 2 different groups. They are enumerated with the index (i=1,2,34,), the consumer groups indexed as 1 and 2 present market A, while groups indexed as 3 and 4 are from market B.

Each group is identified by specific preference over the bundles of goods consisting of x and y. Preferences of representative consumer from the customer segment I (i=1,2,3,4) is described by respective utility function Ui(x,y), x>=0, y>=0. The utility functions Ui(x,y),(i=1,2,3,4) look follows:

U1(x,y) = (x+2y)^0,5

U2(x,y) = (2x+y)^2

U3(x,y) = (4x+3y)^0,75

U4(x,y) = (3x+7y)^1,5

In both markets your company is a price-taker for both products. It provides goods in any amounts demanded by the consumers for given market prices. In market A the price for X is 8, and the price for Y equals 12. Respectively, in market B the price for X and Y equal 24 and 42. Assume that for each segment the firm is aware of the number of consumers Ni and average disposable income Mi representative the consumers type I can spend for purchasing the goods X and Y. The please get done the following assignments and explain the way you do it.

1.Determine the structure of optimal consumption bundle under given prices for X and Y for each type of representative consumer.

2.Estimate the representative consumer demands, consumer group demands and total (market) demands for goods x and y according to the data in the table below

Parameter of variable Price of X Price of Y Demand for X by representative consumer Demand for Y by representative consumer Income M Size of group Group demand for X Group demand for Y