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The Budget Line The line BB gives the persons budget constraint. It is described by the linear equation
c + wl = w;
which can be rewritten as
c = w - wl:
The budget line gives all the consumption-leisure combinations that the person can potentially enjoy with his one unit of time.1 The slope of the budget constraint is given by (the negative of) the wage rate, w. Think about this as representing the relative price of leisure in terms of consumption: if the person desires to enjoy an extra unit of leisure he must sacrifice w in terms of consumption. If the person worked all of his time, so that leisure was zero, then his consumption would be w. This is the vertical intercept of the line. If he did not work, then his leisure would equal one, implying l = 1. He would of course have no consumption, so c = 0. This is the horizontal intercept.
indifference curve and budget line
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