Question
Question 2 (20 marks). Jack consumes only bread (good x) and cheese (good y). His utility function is given by U (x, y) = 4
Question 2 (20 marks). Jack consumes only bread (good x) and cheese (good y). His utility function is given by
U (x, y) = 4 ln x + ln y.
(a) Consider only bundles with both x > 0 and y > 0. Are Jack's preferences monotone? Are they strictly monotone? Does this utility function satisfy diminishing MRS? (5 marks)
(b) Find the expenditure-minimising bundle (x,y) as a function of the prices px and py, and the target utility U. (5 marks)
(c)(c.1) Find the expenditure necessary to attain the utility U as a function of the prices px and py, and the target utility U itself. If the prices are px = 1, py = 1, obtain the expenditure necessary to attain the utility U = ln 32. (3 marks)
(c.2) What is Jack's utility-maximising bundle if his income is M = 5 and prices are px = 1 and py = 1? In a well labelled graph, represent Jack's budget line and his utility-maximising consumption bundle. (2 marks)
(d) Jack's sister, Elena has a utility function given by
V (x, y) = max{2x, y},
where the function max{x, y} gives the maximum of x and y (for instance, max{1, 2} = 2,
max{6, 3} = 6, max{5, 5} = 5, etc.)
(d.1) Provide the utility-maximising consumption bundle as a function of the prices px, py,
and Elena's income, denoted by I. (2 marks)
(d.2) Provide the expenditure-minimising consumption bundle as a function of the prices px,
py , and the target utility V . (2 marks)
(d.3) Suppose that px < py. What is the income elasticity of x? (1 mark)
Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started