Question

In a research paper an economist assumes that the typical consumer has a utility U(X, Y) = X^0.25Y^0.75 and a budget of $1,000.

a) Consider the utility function. What is the consumer’s attitude towards mixing X and Y? What is the shape of the consumer’s indifference curves? Do you expect this consumer to choose a bundle in the interior of the budget line or a bundle at one of the corners? Discuss.

b) Now, turn your attention to the budget set. The price of X is $10 while the price of Y is $25. Write the expression of the budget line and draw the line in an X/Y diagram. Please, if you work on paper use a ruler (your ID card works great). What is the opportunity cost of one unit of X in terms of Y?

c) Find the consumer’s optimal choice using the Lagrangian method. Remember to use the notation economists favor: we explicitly write the expression of the Lagrangian function and then we equate to zero the Lagrangian function’s partial derivatives.

d) In your diagram add an indifference curve to illustrate the consumer’s optimal bundle.

Answer 1

a) The utility function is of the Cobb Douglas type.

Thus, the consumer will prefer to have both x and y with x being equal to 25% of the budget and y being equal to 75% of the budget.

The indifference curve is downward sloping convex to the origin.

Since, the indifference curve is downward sloping convex to the origin, the consumer will prefer a bundle that is interior of the budget line than that in the corners.

b)

Thanks!