Difficult# Consumer Comparatives: Sink or Swim

MICRO-GO@T1L

Andy derives utility from two goods: kitchen sinks and swimsuits. His utility function is:

$$U(K,S) = K^{3/4}S^{1/4}$$

...where $K$ is the number of kitchen sinks he consumes and $S$ is the number of swimsuits. The price of a kitchen sink is $p_K$, the price of a swimsuit is $p_S$, and he has an income of $I$.

The Engel curve shows the relationship between the amount of a good that is consumed and income. For the prices listed below, find the slope of the Engel curve for kitchen sinks at the given prices.