Question

Suppose a consumer views two goods, X and Y, as perfect complements. Her utility function is given by U = MIN [2X, Y]. Sketch the graph of the consumers indifference curve that goes through the bundle X = 5 and Y = 6. Put the amount of Y on the vertical axis, and the amount of X on the horizontal axis. Which of the three assumptions that we made about consumer preferences is violated in this case?

Answer 1

Utility function is given by U= Min(2X,Y)

Because two goods X and Y are perfect complements, then equilibrium is where consumer consume 2X=Y. for any given amount of Y , consumer utility =Y . For additional X, such that 2X>Y doesn't increase utility ,he will consume where 2X=Y.

Indifference curves for thhis utility function are shown below:

IC3 represents the indifference curve when Y=6 and X=3 implies 2X=6. Therefore, X>3 will not increase utility , if the consumer consumes Y=6.

In the case of perfect complements , the indifference curves are no longer smooth but have a kink. And are L-shaped and therefore, contains the points Y=6, X>3 andY>6, X=3.

Therefore, these preferences violates the assumption of more is better and of strict convexity .