Question 1 Let an individual's utility function be given as u(x1, x2) = 2 √ x1 x2
Question
Answered step-by-step
hhh
Question 1 Let an individual's utility function be given as u(x1, x2) = 2 √ x1 x2 . a) Compute the
Marginal Rate of Substitution. b) Initially, the individual consumes bundle (x1 = 100, x2 = 12.5).
Then, the individual's consumption of the first good is cut to x 0 1 = 50
...[Show More]
Question 1 Let an individual's utility function be given as u(x1, x2) = 2 √ x1 x2
Question
Answered step-by-step
hhh
Question 1 Let an individual's utility function be given as u(x1, x2) = 2 √ x1 x2 . a) Compute the
Marginal Rate of Substitution. b) Initially, the individual consumes bundle (x1 = 100, x2 = 12.5).
Then, the individual's consumption of the first good is cut to x 0 1 = 50. What is the new level of
consumption of good 2, x 0 2 , that the individual needs to consume in order to reach the same
utility level as before? c) Given the prices p1 = 1 and p2 = 2 for the first and the second good,
respectively, and a budget of m = 100, what is the best consumer choice? d) Find the individual's
general demand function for good 2. e) If the price for the first good rises to p 0 1 = 50, how
much less of good 2 will the individual conusme? f) Assuming the demand function for good 1 is
x1(p1) = 1 2 m p1 , what is the inverse demand funtion, and what is the own-price elasticity of
demand for good 1! g) Assuming the demand function for good 1 is x1(p1) = 1 2 m p1 , show
mathematically that the good is not inferior.
Question 2 An individual's preferences over consumption bundles A, B, and C are given as A B
B C A C Are these preferences transitive? Explain why or why not!
Question 3 The demand function is given by x = A p-γ with x giving the demand, p the price and
a and γ as positive parameters. a) Derive the price elasticity of demand, ε. What is the economic
meaning of the price elasticity of demand? What is elastic, what is inelastic demand? b) Denote
revenues as a function of demand x and price p. How do revenues change as a reaction to an
increase of the price, if demand is inelastic? c) Is the good in focus a Giffen good? Explain your
answer both verbally and analytically.
There are two consumers who consume good x (private good) and good y (public good).
The sum of consumption between both consumers = T (T1+T2)
price of a private good x= $1
Price of a unit T = $2
Income = $100
Utility function:
U = log X + log(T1 + T2 )
Use the given utility function along with prices, and income to find...
a. socially optimal (efficient) level of production of a public good.
b. market (private) level of provision of a public good
There are two consumers who consume good x (private good) and good y (public good).
The sum of consumption between both consumers = T (T1+T2)
price of a private good x= $1
Price of a unit T = $2
Income = $100
Utility function:
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