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Hi. Please help me to solve this task. I would really like to understand what steps do I need to take to solve it

successfuly. You can see the description and what needs to be done on the first and the second picture. I would really appreciate it if you provide explanations to the steps that can help me to solve this (if the task is too long, please describe the steps that I need to make to solve this task successfully). Thank you very much.

task 2.jpg

task 2 continued.jpg

task 2 continued.jpg

Your company is a price-taker for both products and provides goods in any amounts demanded
by the consumers for given prices. The price for x is given by Px= 15 and price for y equals 10, i.e.,
Py= 10. Assume that for each segment the firm is aware of the number of consumers N, and
average disposable income M; representative consumer of type i can spend for purchasing 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. If disposable incomes are given by M1 = 300; M2 = 180; M3 = 360; M4 = 420; Ms = 540
then what amount of good x and good y will be purchased by each representative
consumer i when Px= 8 and Py= 10.
3. Under given prices for goods and disposable incomes of representative consumers Mi
(i=1,2,3,4,5), the size of each consumer segment is given by number of consumers of
each type N1=3000, N2=4800, N3=4000, N4=2000 and Ns=1200. Then, calculate total
quantities of good x and good y that will be supplied by your company to the market.

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Task 2.
Assume you are managing the company producing two different goods, for certainty, x and y.
Undertaken market research segmented the customer population into 4 different groups. Each
group is identified by specific preference over the bundles of goods consisting of x and y.
Preference of representative consumer from customer segment i (i=1,2,3,4,5) is described by
respective utility function Ui(x,y), x 2 0, y 2 0. The utility functions Ui(x,y), (i=1,2,3,4,5) look as
1. U1(x,y) = 2(3x+5y)0.5;
2. U2(x, V) = --
( 3 * + 5 y ) 2'
3. U3(x,y) = 0.5 e(3x+5y).
4. U4(x,y) = 4(5x+2y)2;
5. Us(x,y) =
(5x+2y) 0.5.

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