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# Consumer equilibrium goods utility given prices given

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Unformatted text preview: , PY w given cost C ( C-bar) isoquant MRTS = -slope cost constraint rK + wL = C The choice problem is to get the highest output level out of the pre-determined expenditures to be spent on inputs. Choose K & L to maximize output f(K,L) subject to rK + wL = C At the point of producer equilib. the isoquant should be tangent to the isocost line. In other words, these two curves should have the same slope. L Isoquant The choice problem is to get the highest utility level out of the pre-determined expenditures to be spent on goods. Choose X & Y to maximize utility U(X,Y) subject to PX X+ PY Y = At the point of consumer equilibrium, the indifference curve should be tangent to the budget line. In other words, these two curves should have the same slope. Indifference curve Y Consumer Equilibrium Producer Equilibrium Budget Line X Isocost Line K 35 CONSUMER EQUILIBRIUM Analytically, the following two equations of consumer equilibrium must be satisfied: MRS = PX PY PX X+ PY Y = Solving these two equations for quantities of goods X and Y demanded, we obtain consumer demands as functions of prices PX , PY, and income, . X = X(PX , PY , ) Y = Y(PX , PY , ) PRODUCER EQUILIBRIUM Analytically, these two equations of producer equilibrium must be satisfied: MRTS = _r_ w rK + wL = C Solving these two equations for quantities of inputs K and L demanded, we get producer demands as functions of prices r , w , and cost, C. K = K(r , w , C) L = L(r , w , C) Now, let's take an example using the simple square root function for both the consumer and the producer. SQUARE ROOT UTILITY On the consumer side, we have the following utility maximization problem: Choose X & Y to maximize utility X0.5Y0.5 subject to PX X+ PY Y = The following two equations of consumer equilibrium must be satisfied: MRS = PX PY PX X+ PY Y = Specifically for the square root utility function, we have: SQUARE ROOT PRODUCTION On the consumer side, we have the following output maximization problem: Choose K & L to maximize output K0.5L0.5 subject to rK + wL = C These two equations of producer equilibrium must be satisfied: MRTS = _r_ w rK + wL = C Specifically for the square root production function, we have: 36 SQUARE ROOT UTILITY Y = PX X PY PX...
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## This note was uploaded on 05/25/2010 for the course ECON 301 taught by Professor Sning during the Spring '10 term at University of Warsaw.

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