What is the best feasible bundle of coke and pepsi

Question

Assignment:

NOTE: You must show ALL of your work for each question. Simply writing the final answer will receive no credit. You may work with others but you must submit your OWN work. Please submit your answers on a separate sheet of paper.

Question 1

A consumer has the following utility function:

U(x₁, x₂) = 1/4 ln(x₁) + 34 ln (x₂) and the following budget constraint:

3x₁ + 2x₂ = 20

a) Find the MRS.

b) Find the price ratio.

c) State the optimality condition.

d) Solve for the best feasible bundle, (x^∗₁, x^∗₂).

Question 2

Suppose the consumer's utility function is U(x, y) = 10xy³ and their budget constraint is 2x + 10y = 200.

a) Find the optimal consumption bundle (x^∗, y^∗).

b) Suppose your income doubles. What is the new optimal bundle?

Question 3

Lily consumes both movie tickets (M) and coffee (C). The price of movie tickets are $6 and the price of coffee is $3. Lily has $35 to spend. Her utility function is given by:

U(M, C) = 5M^1/3 C^2/3

a) Find the optimal bundle of movie tickets and coffee that Lily can consume.

b) What is the new optimal bundle if the price of coffee increases to $4?

Question 4

Logan is planning a party and needs to buy soda. He can either buy Coke or Pepsi and has $50 to spend on soda. The price of Coke is $3 and the price of Pepsi is $2.

Logan is indifferent between Coke and Pepsi (i.e. he has no preference for one or the other) and thus his utility function is given by:

U(C, P) = C + P

a) Write out Logan's budget constraint.

b) What is the best feasible bundle of Coke and Pepsi?

c) Graphically depict the budget constraint, the indifference curves, and the optimal bundle. Make sure to label your axes.

d) How will the optimal bundle change if Coke and Pepsi are the same price?

Question 5

Logan also wants to make hamburgers for his party. To do this, he will need meat and bread. He has $100 to spend on food and the price of a meat patty is $5 and the price of one bread is $2. Each hamburger requires one meat patty and two breads such that his utility function is:

U(M, B) = min{2M, B}

a) Write out Logan's budget constraint.

b) What is the best feasible bundle of meat and buns?

c) Graphically depict the budget constraint, the indifference curves, and the optimal bundle. Make sure to label your axes.

d) Suppose Logan can get a membership card at the store for $15. With the membership, he can buy meat patties for $3 each. What is his new optimal bundle if he buys the membership?

e) Should Logan buy the membership? Why or why not? (Hint: find the total utility under each of the optimal bundles)