Read the scenario below and give a detail response to the questions that follow

Bill, Buster and Bryan share a dormitory room on the UTech campus. The dormitory offers soft drink and chips for sale in vending machines. They consistently choose between soft drink and soda to maximize their satisfaction given their utility function, income and the prices of soda and chips. The table below shows the utility function and income of the dorm mates

Customer Utility Function Income

Bill U(S,C)= S0.3C0.7 $6000

Buster U(S,C)=min(S,3C) $7000

Bryan U(S,C)=2 S + C $4000

A. Given S is the number of soft drinks per week and C the number of bags of chips per week

i. Derive the demand functions for soft drink and chips for BILL. (use both substitution method and Lagrangian method)

(8 marks)

ii. Derive the demand functions for soft drink and chips for BUSTER.(4 marks)

iii. Explain the demand functions for soft drink and chips for BRYAN.(2 marks)

B. If soft drink is priced at $100 each, chips $50 per bag per week to spend on chips and soft drink,

i. Complete the table showing the optimal amount of soft drink (S*) and chips (C*) and utility value (U*) for each person?

(4 marks)

S* C* U*

Bill

Buster

Bryan

ii. Suppose income increase by 50% for each person

a) Draw BILL'S income-offer and Engel curves for both goods.(6 marks)

b) Illustrate BUSTER'S income-offer curve and Engel curve for both goods

(6 marks)

C. Suppose the price of chips increase from $50 to $100 and income remain constant

a) Draw BILL'S price offer curve and demand curve.(6 marks)

b) Draw BUSTER'S price offer curve and demand curve.(6 marks)

c) Illustrate BILL'S income and substitution effect(4 marks)

d) What is the income and substitution effect for BUSTER and BRYAN?

(4 marks)