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Unformatted text preview: hich is the expenditure function! Expenditure Minimization (Dual) Using the dual formulation of expenditure minimization, we have the following two equations of consumer equilibrium: MRS = _PX_ = 3Y PY X U(X,Y) = X0.75Y0.25 = Solving these two equations, we get the demands for X & Y 3Y = _1_ 6Y = X (6Y)0.75Y0.2 = 60.75 Y0.75 Y0.25 = 3.833658625Y= X 2 So, Y = __________ 3.833658625 or simply, Y = 0.26084743 3Y = _1_ 6Y = X Y = 0.1666X X0.75(0.1666X)0.25 = X 2 (0.1666)0.25 X0.75 X0.25 = 0.638943104X = 46 So, X = __________ 0.638943104X
ASIDE: or simply, X = 1.565084581 Once we had the demand for good Y, Y = 0.26084743 , we could have simply taken the relationship X = 6Y and calculated: X = 6(0.26084743 ) = 1.565084580 (difference in 9th decimal place is due to machine imprecision). BACK TO OUR REGULARLY SCHEDULED PROGRAMMING!! Substituting these factor demands into the budget constraint, we get the expenditure term as a function of the utility level. I = PXX + PYY = X + 2Y = 1.565084581 + 2(0.26084743 ) = 1.565084581 + 0.52169486 = 2.086779441 Rearranging the result so that the utility term is on the left hand side, we get the utility level as a function of the income(expenditure) term. = _____I_____ 2.086779441 = 0.479207328 I SAME AS THE RESULTS FROM THE UTILITY MAXIMIZATION PROBLEM!!!!
FACTOR MARKETS Factor markets, especially labour and human capital, have some peculiar features that deserve some special attention. We will consider factor market pricing in the labour market under perfect competition and imperfect competition. So how do we price labour in a competitive market? 47 Just as in any other market, pricing in a competitive labour market is a result of balancing two opposing forces...the demand side (producers/firms that wish to employ labour) and the supply side (consumers/workers that wish to offer labour services). [Demand for Labour by Firms] [Supply of Labour by Consumers] Labour Market Let's look at each side separately in order to derive the demand for labour by firms and the supply of labour by workers. Demand for Labour The demand for labour can be derived f...
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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.
- Spring '10