Income and Substitution Effects Econ

We have already introduced the notions of MRT coming out of the budget constraint and MRS 1 coming from a consumer’s preferences. In our discussion of the consumer’s problem we talked about how, for example, if MRS < MRT at a point on the budget line, it means that the consumer is willing to give up good 2 for good 1 at slower rate than the market. Or put another way, the market put a lower value on good 2 than the consumer at that point, which means the consumer can improve welfare by trading in good 1 for good 2 at the market rate of exchange. It is the ratio of the prices that determines the MRT and therefore determines the optimal location along the budget line for the consumer. The problem, however, is that if we start from one solution point under a particular budget and a price changes, the MRT is not the only thing to change. One cannot change the slope of a line without changing its entire position, save one point. For the typical price change, that one point is an intercept which means, from the point of view of the previous solution point, the price change includes a significant wealth or income effect. We are going to imagine the this change in the budget line from a price change taking place in two steps: (i) a rotation to the new MRT pivoting through the original choice (and therefore stripping away the income effect) followed by (ii) a parallel shift from there out (or in) to the new budget line which adds back the income effect we stripped away in the rotation. First the rotation pivoting through the original choice ... Imagine standing on our “hill of happiness” at the original solution point. You are right on top of the fence-line (budget line) at its highest point on the hill. Now somebody changes the angle at which that fence goes across the side of hill by rotating it around the point you are standing on. With this