
Posted: 2/15/2013 8:08:21 AM EDT
bump



Posted: 2/16/2013 9:53:17 AM EDT
You could use the CobbDouglas production functions as a simple example:
(1) C = ALCaTC1a and (1â€™) F = BLFbTF1b, where C(F) is the quantity of clothing (food) being produced, LC(LF) is the quantity of labour employed in cloth (food) production, and TC(TF) is the quantity of land employed in cloth (food) production. The coefficient A(B) is a positive constant reflecting technology. First, define the unit isoquants, showing the amount of land used given the employment of labour in producing each unit of cloth (food). These are: (2) TC = [A1LCa]1/(1a) and (2â€™) TF = [B1LFb]1/(1b) .(1) The firstorder conditions, coupled with linear homogeneity, allow the derivation of lines that show factor price ratios that are consistent with various input combinations. Following Krugman and Obstfeld, these are denoted as CC and FF respectively. The equation for the line CC (the cloth industry's expansion path) is: (3) r = (1/a1)(LC/TC)w , where w is the wage rate (payment per unit of labour) and r is the rental rate (per unit of land). The corresponding FF line, similarly defined, is: (3â€™) r = (1/b1)(LF/TF)w. So far, the model transforms the expansion paths in the two industries into equations involving factor prices in each of the two industries. To move closer to closing the model requires that product prices be related to the information above. This is accomplished by imposing equilibrium conditions for competitive markets, that price equals marginal cost (MC) in each industry. Since MC = w/MPL in each industry, this imposition implies the following: (4) PC = w(Aa)1(1/a1)a1(w/r)a1 and (4â€™) PF = w(Bb)1(1/b1)b1(w/r)b1. These two equations provide this critical relationship between the ratio of input prices and that of product prices: (5) (w/r) = [Aa(1/a1)1a(Bb1)1(1/b1)b1(PC/PF)]1/(ab). Determining how much labour and land are used in each of the two industries can now close the model. The expansion paths give the key to this determination. (6) TC = (w/r)(1/(a1))LC and (6â€™) TF = (w/r)(1/(b1))LF. But, LF = LLC and TF = TTC. Appropriate substitution allows TC and TF to be stated as a linear function of LC. The resulting equations are: (7) TC = kLC and (7') TF = mLmLC where k=(w/r)(1a)/a and m = (w/r)(1b)/b. 


Posted: 2/16/2013 10:10:56 AM EDT
Why are you doing an Edgeworth? Someone wants to show whats "fair" instead of Pareto efficent?



Posted: 2/16/2013 2:49:32 PM EDT
[Last Edit: 2/16/2013 2:50:41 PM EDT by CouchCommando]
I figured out a decent looking solution by just using lines for the other edges. I used CobbDouglas functions to illustrate the point.
My primary study strategy is rewriting notes. I've been taking it one step further by typing them in LaTex after rewriting them. We just finished general equilibrium theory and are moving on to game theory, which will be a little harder to represent in excel. ETA: My professor called the 1st welfare theorem the Republican welfare theorem, and the second welfare theorem the Democratic welfare theorem. While I don't think it helped the Chinese students too much, it certainly helped me memorize them on the spot. 


Posted: 2/16/2013 3:04:11 PM EDT



