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Unformatted text preview: precision). BACK TO OUR REGULARLY SCHEDULED PROGRAMMING!! or simply, K = 1.319507911Q Substituting these factor demands into the cost constraint, we get the cost term as a function of the output level. 42 C = rK + wL =K+L = 1.319507911Q + 0.329876977Q = 1.64938489Q Rearranging the result so that the output term is on the left hand side, we get the output level as a function of the cost term. Q = _____C_____ 1.64938489 = 0.606286626C SAME AS THE RESULTS FROM THE OUTPUT MAXIMIZATION PROBLEM!!!!
DUALITY OF UTILITY AND EXPENDITURE As in the investigation of production and cost, there are also many similarities between the theory of utility maximization and expenditure minimization. That is, an efficient consumer must consider the following twin problems: On one hand, in terms of utility, a consumer needs to consider the primal problem of producing the highest level of utility for a fixed budget constraint (utility maximization problem). On the other hand, in terms of expenditure, the same consumer needs to consider the dual problem of keeping the lowest level of expenditure for a fixed utility level (expenditure minimization problem). UTILITY MAXIMIZATION EXPENDITURE MINIMIZATION The primal problem is to get the highest The dual problem is to get the utility possible from a given expenditure level. lowest expenditure level required to produce a given utility level. That is, for a given level of income, , the consumer must choose X & Y to maximize utility, U. For a given level of utility, , the consumer must choose X & Y to minimize expenditure, I. 43 Choose X & Y to maximize utility U(X,Y) subject to PXX + PYY = Y Choose X & Y to minimize expenditure PXX + PYY = I subject to U(X,Y) = Y Highest IC for a given budget line Lowest BL for a given indifference curve X X Objective: Highest indifference curve Constraint: Fixed budget line As before, we need to satisfy two conditions of consumer equilibrium. MRS = _PX_ PY PXX + PYY = Solving these two equations, we get the consumer demands for X & Y as functions of prices PX , PY , and income level, . X = X(PX , PY , ) Y = Y(PX , PY , ) If we substitute these demands into th...
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- Spring '10