G: Consider a two agent exchange economy with agents A and B having distinct Cobb-Douglas preferences, uA(x1;x2) = alnx1 +(1 a)lnx2; uB(x1;x2) = blnx1 +(1 b)lnx2 for a; b 2 (0; 1). Suppose that there...

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   G: Consider a two agent exchange economy with agents A and B having distinct Cobb-Douglas preferences,
   

   
   

   uA(x1;x2) = alnx1 +(1 a)lnx2; uB(x1;x2) = blnx1 +(1 b)lnx2
   

   
   

   for a; b 2 (0; 1). Suppose that there are equal endowments, eA1 ;eA2 = eB1 ;eB2 = (1;1):
   

   
   
   
   
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      (a) Compute total market demand for good 1 as a function of the priceofgood1,p1 2(0;1),wherep2 =1 p1.
      

      
      
   
   
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      (b) Identify the equilibrium price of good 1, p 1, where p2 = 1 p1.
      

      
      
   
   
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      (c) Identify x^A(p 1), the equilibrium allocation of goods to agent A.
      

      
      
   
   
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      (d) Identify x^B(p 1), the equilibrium allocation of goods to agent B.
      

      
      
   
   
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      (e) Illustrate this equilibrium in the Edgeworth box by drawing the corresponding budget set and indi§erence curves for the special case a = 0:75, b = 0:25.
      

      
      
   
   
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      (f) Mark the set of all Pareto improvements over the endowment point (also known as ìthe cigar of gains from tradeî).
      

      
      
   
   
   
   


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   R: Consider a two agent exchange economy with agents A and B both having the same quasi-linear preferences,
   

   
   

   uA;B(x1;x2)=lnx1 +x2: Now suppose that the endowments satisfy,
   

   
   

   
   eA1 ;eA2 = eB1 ;eB2 = (1;z): for z > 0.
   

   
   
   
   
   1. 
      

      (a) Compute total demand for good 1 as a function of the price of good1,p1 2(0;1),wherep2 =1 p1.
      

      
      
   
   
   2. 
      

      (b) Identify the equilibrium price of good 1, p 1. 1

      
      
   
   
   
   

Intermediate Microeconomics UA10 Homework 6 Fall 2019 Due in Recitation Friday October 18 1. G: Consider a two agent exchange economy with agents A and B having distinct Cobb-Douglas preferences, uA(x1, x2) = a lnx1 + (1− a) lnx2; uB(x1, x2) = b lnx1 + (1− b) lnx2 for a, b ∈ (0, 1). Suppose that there are equal endowments,( eA1 , e A 2 ) = ( eB1 , e B 2 ) = (1, 1) . (a) Compute total market demand for good 1 as a function of the price of good 1, p1 ∈ (0, 1), where p2 = 1− p1. (b) Identify the equilibrium price of good 1, p∗1, where p2 = 1− p1. (c) Identify x̂A(p∗1), the equilibrium allocation of goods to agent A. (d) Identify x̂B(p∗1), the equilibrium allocation of goods to agent B. (e) Illustrate this equilibrium in the Edgeworth box by drawing the corresponding budget set and indifference curves for the special case a = 0.75, b = 0.25. (f) Mark the set of all Pareto improvements over the endowment point (also known as “the cigar of gains from trade”). 2. R: Consider a two agent exchange economy with agents A and B both having the same quasi-linear preferences, uA,B(x1, x2) = ln x1 + x2. Now suppose that the endowments satisfy,( eA1 , e A 2 ) = ( eB1 , e B 2 ) = (1, z) . for z > 0. (a) Compute total demand for good 1 as a function of the price of good 1, p1 ∈ (0, 1), where p2 = 1− p1. (b) Identify the equilibrium price of good 1, p∗1. 1