Question

Suppose a consumer views two good, 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 = 4. 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

$$Solution$$

The utility function is given by $U=Min(2X,Y)$

Because two goods $X$ and $Y$ are perfect complements, then equilibrium will be obtained 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 $2X=Y$ .

The Indifference curves for this utility function are shown below:

$IC3$ represents the indifference curve when $Y=4$ and $X=2$ implies $2X=4$ . Therefore, $X>3$ will not increase utility , if the consumer consumes $Y=4$ .

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 $Y=4$ , $X>2$ and $Y=4$ , $X=2$ .

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