mmacroecon

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 with x giving the demand, p the price and a and as positive parameters. a) Derive the price elasticity of demand, . 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.

Exercise 1 (Training and payment system, By Kim Swales) Two players: The employee (Raquel) and the employer (Vera). Raquel has to choose whether to pursue training that costs 1, 000 to herself or not. Vera has to decide whether to pay a fixed wage of 10, 000 to Raquel or share the revenues of the enterprise 50:50 with Raquel. The output is positively affected by both training and revenue sharing. Indeed, with no training and a fixed wage total output is 20, 000, while if either training or profit sharing is implemented the output rises to 22, 000. If both training and revenue sharing are implemented the output is 25, 000. 1. Construct the pay-off matrix 2. Is there any equilibrium in dominant strategies? 3. Can you find the solution of the game with Iterated Elimination of Dominated Strategies? 4. Is there any Nash equilibrium?

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

[9:23 PM, 12/8/2021] Fridah: 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. [9:25 PM, 12/8/2021] Fridah: 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.