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Unformatted text preview: r markets, the key implication is that firms are price takers in both the output and the input markets (sell at P determined in the market, pay labour w determined in the market). Recall that we have only one variable input, labour, in our investigation and the production function is: Q = f (L) It is important to remember the goal of the producer under perfect competition is to maximize profits as follows: f (P,w) = max PQ wL subject to Q = f (L) Q,L f (P,w) = max P f (L) wL L FOC: (P,w) = 0 L  FOC: Pf(L) w = 0 This characterizes the optimal solution. Pf(L) w = 0 Pf(L) = w 49 or, MP P = w MRP = w MRP = MCL  FOC: Pf(L) w = 0 Pf(L) = w f(L) = __w__ P MP = __w__ P MP = real wage  FOC: Pf(L) w = 0 Pf(L) = w P = __w__ f(L) MRQ = MCQ The decision rule based on dollar values turns out to be exactly the same as the decision rule based on physical units (because they are variations on the same expression). In  above, we can see that price is the ratio of w and MPL (which is the marginal cost of producing one additional unit of Q). We can also see, under perfect competition, P = MR so we get the familiar optimal condition under perfect competition where P = MC. or, or, 50 Slope = w / P Q f (L) w / P = f (L) = PQ wL Q = / P + (w / P) L L Let's do a simple example. Consider the square root production function with only the labour input. Q = L1/2 The MPL is: MPL = __1__ 2 L1/2 Now, suppose that we are in a competitive setting and the price of output is P = 24 and the price of labour is w = 4. We can derive the optimal amount of labour demanded by the firm using the decision rule either in terms of physical units or in terms of dollar values as: PHYSICAL UNITS Optimal Decision Rule MPL = __w__ P __4__ = __1__ 24 2 L1/2 8 L1/2 = 24 L1/2 = 3 L=9 51 DOLLAR VALUES Optimal Decision Rule MRP = w __1__ 24 = 4 2 L1/2 8 L1/2 = 24 L1/2 = 3 L=9 MP Physical Units $ MR w/P w L 9 9 L The Demand Curve for Labour The example above gives us the quantity of labour demanded at a market wage of $4. If we vary the values of the market wage, w, and calculate the corresponding labour quantities demanded by the firm, we get the derived demand curve for labour by the firm. Using the above example, we get the labour demand equation as: PHYSICAL UNITS Optimal Decision Rule MPL = __w__ P _...
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- Spring '10