Overview In consumer theory we started with the x and y axes both referring to a good or service, with each axis representing a different specific good. Sometimes, though, we only want to focus on one good against everything else we could buy. If we think of the Y good as a composite commodity then we can say the price of the good is $1 per unit and the commodity is really then how much we spend on all goods except good x. The budget line and indifference curves we saw before are essentially the same as we saw before.
Budget line Before we said the budget line was PxX + PyY = I, with vertical intercept = I/Py, horizontal intercept = I/Px and slope –Px/Py. In the context of the composite commodity we have PxX + Y = I, with vertical intercept = I (our income amount), horizontal intercept = I/Px still and slope = -Px Y I X I/Px
Utility max With the composite good our utility max story is the same as before except when we see point X1 the Y point is the amount of income we have left after buying X1 units of X. The point of the composite commodity idea is we can focus on the x good and everything else in a lumped up amount. Y I – PxX1 X X1