Two individuals, A and B, are free to engage in trade of clothing and food. Initially, A has 12 units of clothing and 9 units of food, and B has 8 units of clothing and 11 units of food. The individuals have the following utility functions in clothing C and food F:
U_A = 0.15Q_C ∙ Q_F
U_B = 0.08Q_C ∙ Q_F
where Q_F represents units of food, Q_C represents units of clothing, and U represents utility. Determine if a mutually beneficial trade is possible between A and B. If so, who would trade for what?

Question

Alice Gathoni · Accepted Answer

Final Answer : If, and only if, an efficient allocation exists, the MRS A  of clothing for food for A will equal the MRS B  of clothing for B.  A  of clothing for food for A will equal the MRS B  of clothing for B.   =   =   =   =   =   = 0.75   =   =   = 1.375 In this situation the MRS for A does not equal MRS for B; consequently there is a potential for mutually beneficial trade. Individual A is willing to give up at most 0.75 units of food to get one additional unit of clothing. Individual B is willing to give up at most 1.375 units of food to get one unit of clothing (or give up 0.727 units of clothing to get one unit of food). Therefore a mutually beneficial exchange can be made. A would trade clothing for food and B would trade food for clothing. The terms of trade would be between 0.75 and 1.375 depending upon the exact bargaining process. class=answers-bank-image d-inline rel=preload > =  A  of clothing for food for A will equal the MRS B  of clothing for B.   =   =   =   =   =   = 0.75   =   =   = 1.375 In this situation the MRS for A does not equal MRS for B; consequently there is a potential for mutually beneficial trade. Individual A is willing to give up at most 0.75 units of food to get one additional unit of clothing. Individual B is willing to give up at most 1.375 units of food to get one unit of clothing (or give up 0.727 units of clothing to get one unit of food). Therefore a mutually beneficial exchange can be made. A would trade clothing for food and B would trade food for clothing. The terms of trade would be between 0.75 and 1.375 depending upon the exact bargaining process. class=answers-bank-image d-inline rel=preload > =  A  of clothing for food for A will equal the MRS B  of clothing for B.   =   =   =   =   =   = 0.75   =   =   = 1.375 In this situation the MRS for A does not equal MRS for B; consequently there is a potential for mutually beneficial trade. Individual A is willing to give up at most 0.75 units of food to get one additional unit of clothing. Individual B is willing to give up at most 1.375 units of food to get one unit of clothing (or give up 0.727 units of clothing to get one unit of food). Therefore a mutually beneficial exchange can be made. A would trade clothing for food and B would trade food for clothing. The terms of trade would be between 0.75 and 1.375 depending upon the exact bargaining process. class=answers-bank-image d-inline rel=preload > =  A  of clothing for food for A will equal the MRS B  of clothing for B.   =   =   =   =   =   = 0.75   =   =   = 1.375 In this situation the MRS for A does not equal MRS for B; consequently there is a potential for mutually beneficial trade. Individual A is willing to give up at most 0.75 units of food to get one additional unit of clothing. Individual B is willing to give up at most 1.375 units of food to get one unit of clothing (or give up 0.727 units of clothing to get one unit of food). Therefore a mutually beneficial exchange can be made. A would trade clothing for food and B would trade food for clothing. The terms of trade would be between 0.75 and 1.375 depending upon the exact bargaining process. class=answers-bank-image d-inline rel=preload > =  A  of clothing for food for A will equal the MRS B  of clothing for B.   =   =   =   =   =   = 0.75   =   =   = 1.375 In this situation the MRS for A does not equal MRS for B; consequently there is a potential for mutually beneficial trade. Individual A is willing to give up at most 0.75 units of food to get one additional unit of clothing. Individual B is willing to give up at most 1.375 units of food to get one unit of clothing (or give up 0.727 units of clothing to get one unit of food). Therefore a mutually beneficial exchange can be made. A would trade clothing for food and B would trade food for clothing. The terms of trade would be between 0.75 and 1.375 depending upon the exact bargaining process. class=answers-bank-image d-inline rel=preload > =  A  of clothing for food for A will equal the MRS B  of clothing for B.   =   =   =   =   =   = 0.75   =   =   = 1.375 In this situation the MRS for A does not equal MRS for B; consequently there is a potential for mutually beneficial trade. Individual A is willing to give up at most 0.75 units of food to get one additional unit of clothing. Individual B is willing to give up at most 1.375 units of food to get one unit of clothing (or give up 0.727 units of clothing to get one unit of food). Therefore a mutually beneficial exchange can be made. A would trade clothing for food and B would trade food for clothing. The terms of trade would be between 0.75 and 1.375 depending upon the exact bargaining process. class=answers-bank-image d-inline rel=preload > = 0.75  A  of clothing for food for A will equal the MRS B  of clothing for B.   =   =   =   =   =   = 0.75   =   =   = 1.375 In this situation the MRS for A does not equal MRS for B; consequently there is a potential for mutually beneficial trade. Individual A is willing to give up at most 0.75 units of food to get one additional unit of clothing. Individual B is willing to give up at most 1.375 units of food to get one unit of clothing (or give up 0.727 units of clothing to get one unit of food). Therefore a mutually beneficial exchange can be made. A would trade clothing for food and B would trade food for clothing. The terms of trade would be between 0.75 and 1.375 depending upon the exact bargaining process. class=answers-bank-image d-inline rel=preload > =  A  of clothing for food for A will equal the MRS B  of clothing for B.   =   =   =   =   =   = 0.75   =   =   = 1.375 In this situation the MRS for A does not equal MRS for B; consequently there is a potential for mutually beneficial trade. Individual A is willing to give up at most 0.75 units of food to get one additional unit of clothing. Individual B is willing to give up at most 1.375 units of food to get one unit of clothing (or give up 0.727 units of clothing to get one unit of food). Therefore a mutually beneficial exchange can be made. A would trade clothing for food and B would trade food for clothing. The terms of trade would be between 0.75 and 1.375 depending upon the exact bargaining process. class=answers-bank-image d-inline rel=preload > =  A  of clothing for food for A will equal the MRS B  of clothing for B.   =   =   =   =   =   = 0.75   =   =   = 1.375 In this situation the MRS for A does not equal MRS for B; consequently there is a potential for mutually beneficial trade. Individual A is willing to give up at most 0.75 units of food to get one additional unit of clothing. Individual B is willing to give up at most 1.375 units of food to get one unit of clothing (or give up 0.727 units of clothing to get one unit of food). Therefore a mutually beneficial exchange can be made. A would trade clothing for food and B would trade food for clothing. The terms of trade would be between 0.75 and 1.375 depending upon the exact bargaining process. class=answers-bank-image d-inline rel=preload > = 1.375In this situation the MRS for A does not equal MRS for B; consequently there is a potential for mutually beneficial trade. Individual A is willing to give up at most 0.75 units of food to get one additional unit of clothing. Individual B is willing to give up at most 1.375 units of food to get one unit of clothing (or give up 0.727 units of clothing to get one unit of food). Therefore a mutually beneficial exchange can be made. A would trade clothing for food and B would trade food for clothing. The terms of trade would be between 0.75 and 1.375 depending upon the exact bargaining process.

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