Question

Diana's utility function for consuming apples (Xa) and Bananas (Xb) is U(Xa,Xb) = XaXb.

Suppose the prices of apples is $1, bananas $2, and her income is $40.

1. 1. On a graph with bananas on the y-axis, use blue ink to draw Bianca’s budget line.With red ink, plot an indifference curve that gives her a utility level of 150. Using black ink, plot an indifference curve that gives her a utility level of 300.
2. 2. Can Bianca afford any bundles that give her utility of 150? Can she afford any bundles that give her utility of 300?
   3. On your graph, mark a point that gives Bianca higher utility than 150 that she can afford. Label that point A.
   4. Write an equation that implies that Bianca’s budget constraint is tangent to her indifference curve at the point (?1, ?1).
3. 5. Find the best bundle that Bianca can afford and label it E on your graph. How many apples and bananas is Bianca consuming at this point?

Answer 1

a. The consumer's utility function is:

The consumer's budget line is given by:

Plotting the consumer's indifference curves for 150 and 300 levels of satisfaction along with the consumer's budget line:

The green curve is the consumer's budget line, the purple curve is the indifference curve for satisfaction level of 300 and the red curve is the indifference curve for satisfaction level of 150.

b. The consumer can afford bundles which give her utility of 150 as a part of the indifference curve lies in the consumer's budget set (lower contour of the consumer's budget line). The consumer cannot afford any bundle which gives her a utility of 300 as the indifference curve does not intersect the budget line at any point.

c. Labeling the required point:

On this point, the consumer is on a higher indifference curve which provides her with higher satisfaction than 150.

d. For the indifference curves and budget line to be tangential to each other, the marginal rate of substitution is equal to the price ratio:

e. Substituting this into the consumer's budget equation:

Plotting this point on the consumer's budget line:

The consumer consumes 20 apples and 10 bananas.