Consider some consumer who consumes good $x$ and $y$. The price of $x$ is fixed to be $k$. The price of $y$ is $c(y)$. The consumer's marginal rate of substitution is given by $\frac{-x}{y}$. If the consumer optimises and is a price taker, I know she should set the absolute value of this equal to the price ratio. However, her quantity demanded affects the price ratio, as her demand influences the price of $y$. So, does it still hold that she would set
$$\frac{x}{y}=\frac{k}{c(y)}$$
Or does this result fail since her quantity demanded has an affect on the price of $y$?