Consumption一 budgets The MRS Condition In the case on the last slide the solution to the consumer's problem is interior - optimal choice is given by a tangency condition. The slope of the budget line at the solution is equal to the slope of the indifference curve. Recall both slopes had an interpretation. ratio and one the marginal rate of substitution. MRS=_p1 If preferences ex and monotonic and the above MRS condition is satisfied at a particular point then that point represents the optimal choice for the consumer. With convex preferences the tangency condition is sufficient for optimality. The condition itself says that the internal(private)rate of exchange- the MRS- equals the external (market) rate of exchange - the price ratio Everyone consuming the goods has the same MRS regardless of their preferences. Consumption- Budgets The MRS condition is not necessary for a solution with convex and monotonic preferences. In other words. a point which represents an optimal choice does not imply the tangency condition at that point x=0 In the first graph there is a solution- sometimes called a boundary solution. In the second graph. optimal solution with a"kinky" indifference curve need not correspond to a tangency. These examples have convex preferences. If preferences are non-convex the tangency condition is no longer sufficientConsumption — Budgets 9 The MRS Condition • In the case on the last slide the solution to the consumer’s problem is interior — optimal choice is given by a tangency condition. The slope of the budget line at the solution is equal to the slope of the indifference curve. • Recall both slopes had an interpretation, one was the price ratio and one the marginal rate of substitution. MRS = − p1 p2 • If preferences are convex and monotonic and the above MRS condition is satisfied at a particular point then that point represents the optimal choice for the consumer. • With convex preferences the tangency condition is sufficient for optimality. The condition itself says that the internal (private) rate of exchange — the MRS — equals the external (market) rate of exchange — the price ratio. • Everyone consuming the goods has the same MRS regardless of their preferences. Consumption — Budgets 10 Corner Solutions • The MRS condition is not necessary for a solution with convex and monotonic preferences. In other words, a point which represents an optimal choice does not imply the tangency condition at that point. . ................................................................................................................................................................................................................................................... . ................................................................................................................................................................................................................................................................................ . ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ........ . ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ...... ................................................................................................................................................................................................................................................................................. . . . . ............. ............. ............. ............. ......... x2 x1 x2 x x1 ∗ 2 = 0 x ∗ 1 x ∗ 2 x ∗ 1 0 . ........ ........ ..... . ........ ........ ..... ...... ..... ..... ..... ..... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...... ..... .... .... .... .... .... ... ... ... ... ... ... ... ... ... ... ... .. .. .. • In the first graph there is a corner solution — sometimes called a boundary solution. In the second graph, an optimal solution with a “kinky” indifference curve need not correspond to a tangency. • These examples have convex preferences. If preferences are non-convex the tangency condition is no longer sufficient