464math2

# 464math2 - M. Muniagurria Econ 464 MICROECONOMIC HANDOUT...

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q M 1 2 L M q M q F 10 40 /46 UNQRG QH 22( UNQRG QH 22( /2. / /2. ( ±²± 691³5’%614³’%101/;´³241&7%6+10³5+&’ M. Muniagurria Econ 464 MICROECONOMIC HANDOUT (Part 2) V. (1) Case of one input : L (Labor) - Assume 2 produced goods: M & F - Fixed amount of labor: L (Needs to be allocated to the 2 sectors) - Firms maximize profits taking prices (P & P ) and wages (w) as given. MF (a) Linear Production Functions Example: Assume: q = ½ L , q = 2 L , L = 20 MM F F Here MPL = ½ MPL = 2 Unit labor coeff: a = 2 a = ½ LM LF Then we can draw the PPF (Production Possibility Frontier) (combinations of q & q that can be M F produced using the 20 units of labor available : 20= a . q + a . q = 2 . q + 1/2 . q ): M F M F Definition : Also true that We need to figure out:

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S / t ; R / & R ( R / S ( q M q F 40 10 Isovalues PPF S / ; R / & R ( R / S ( ±²± (i) - How many units of q & q will profit max. firms produce? FM (ii) - How is labor allocated across sectors? Remark 1 : If you know the answers to one question, you can answer the other. (i) It is a good idea in this case to think of an economy with only one firm. If the firm knows how to produce both goods, profit maximization is equivalent to maximize the value of production subject to the technology constraint (PPF) i.e.: maximize Y = p . q + p . q Subject to PPF in Diagram 1 MM FF Value of production We can also write the previous equation as: Isovalue lines : Lines along which the value of output is constant (Y is a constant).
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## 464math2 - M. Muniagurria Econ 464 MICROECONOMIC HANDOUT...

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