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Unformatted text preview: _w__ = __1__ 24 2 L1/2 2w L1/2 = 24 L1/2 = 12 / w L = 144 / w2 DOLLAR VALUES Optimal Decision Rule MRP = w __1__ 24 = w 2 L1/2 2w L1/2 = 24 L1/2 = 12 / w L = 144 / w2 52 w w L = 144 / w2 L = 144 / w2 L L HOMEWORK 1. Formulate and solve the utility maximization problem for the general CobbDouglas utility function U(X,Y) = XY And confirm that the consumer demands are: X = ______ [I / PX] + and Y = ______ [I / PY] + 2. Formulate and solve the output maximization problem for the general CobbDouglas production function f(X,Y) = KL And confirm that the factor demands are: K = ______ [C / r] + and L = ______ [C / w] + 3. Using your results from question 2, verify that the cost function is if + = 1. C = _Q_ [r / ] [w / ] 4. Consider a production function with only the labour input. If the wage rate is $17 per hour and the price of output is $153, what is the demand for labour if we assume that all markets are competitive. Find the demand for labour using the method shown for physical quantities and then confirm your answer by finding demand for labour using the method shown for dollar values if the production function is defined as Q = L1/5. 53 ECON 301 LECTURE #4 Market Demand for Labour The market demand curve for labour is obtained by the usual horizontal summation technique. This involves adding up all of the individual firm's demands for labour along the horizontal axis. $ Market Demand Curve for Labour d1 d2 d4 d3 L Now, suppose we have a production function f (L) = ln(1+L). What is the firm's demand for labour, in general? Using the firm's profit function we can find the profit maximizing labour input... Max {P ln(1 + L) wL} FOC __P__ = w 1+L P/w=1+L L = (P w) w In general, we can say that for any number of inputs i = 1, 2, ... , n P MPi = wi P MPL = w P MPK = r P MPLAND = t (rental rate of land), etc. 54 Labour Supply The supply of labour is derived from the consumer's problem of choosing between work and PLAY!!! Work (BOOOO!!!!) yields income, while play (OH YEAHHHHH!!!) gives us utility in the form of leisure. We formulate this pr...
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 Spring '10
 sning
 Economics

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