Assume you are managing the company producing two different goods, for certainty, x and y. The company sells the products x and y in two local markets, for certainty, denoted as market A and market B. Marketing research segmented the customer population in each local market into 2 different groups. They are enumerated with index i (1=1,2,3,4), the consumer groups indexed as 1 and 2 come from 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 commodities x and y. Preference of representative consumer from the customer segment 1 (1=1,2,3,4) is described by respective utility function Ui(x.y), x 2 0, y 2 0. The utility functions Ui(x.y). (i=1,2,3,4) look as follows: 1. U1(x,y) = (x + 2y)0.5; 2. Uz(x,y) = (2x + y)2; 3. Us(x,y) = (4x + 3y)0.75. 4. U4(x,y) = (3x + 7y)0.85. Assume you are a top manager responsible for sales in the company. In each market (A and B) 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 (P.^= 8) and price for y equals 12 (PyA= 12). Respectively, in market B the prices for x and y equal PB = 24 and PB = 42. Assume that for each segment the firm is aware of the number of consumers Ni and average disposable income Mi representative consumer of type i can spend for purchasing the goods x and y. Then, 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.Group 1 Group 2 Group 3 Group 4 Total Parameter or variable price of x 8 8 24 24 N/A price of y 12 12 42 42 N/A demand for x by representative consumer demand for y by representative consumer income M 320 480 480 504 N/A size of group 200 250 250 200 N/A group demand for x group demand for y Please, fill in the answers into the table and explain your estimations with respective formulas and definitions of variables. 3. Construct the total market (i.e., in markets A and B) demand curve for product x. Show solution on the diagram with price at vertical axis 4. Construct the total market (i.e., in markets A and B) demand curve for product y. Show solution on the diagram with price at vertical axis
