How Does Market Power Affect the Consumer's Rate of Exchange?

[mrroboto]

Homework Statement

Since consumers cannot be outside the set of affordable bundles, we get the rate of exchange that consumers face provided the spend all of their budget

dy/dx = -Px/Py (where Px is the price of good x, PY is the price of good y)

by totally differentiating the budget constraint and requiring that dm = 0, where m is total income. Suppose now that the consumer is a price taker in the x market but not a price taker in the y market. What is the rate of exchange that the market offers the consumer?

Homework Equations

dy/dx = -Px/Py
m = Px(X) + Py(Y), where X and Y represent total number of goods X and Y, respectively.

The Attempt at a Solution

I know I have to totally differentiate the budget constraint. In other words, I take the derivative of the equation m = Px(X) + Py(Y). Then I have to figure out how altering the quantity of Y with affect Py, the price of Y.

By rearranging the equation m = Px(X) + Py(Y), I get Y = (-Px/Py)(X) + m/Py, and since dm= 0, we arrive at the equation dy = (-Px/Py)dx.

I don't know what to do from here. Can someone please help?

 

[mrroboto]

nevermind. i got it.