1. Kamal (K) and Jamal (J) are the only two individuals in an exchange economy consisting of only two goods, namely 100 units of mangoes (m) and 100 units of guavas (g). The utility functions of Kamal and Jamal are represented by (m+8x)=m*g* and U, (m,.g,)=m, g3 respectively. Furthermore, m + m, 100 and gx + g = 100. 3/4 1/4 3/4 UK (a) Show that the efficient allocation of mangoes and guavas for Jamal is given by the following condition 8, 9m, 100-g, 100-m, (Hint: Let Kamal's utility be fixed at U, then solve the Lagrangian L=U, (m,.g,) + 2[U (m.8)-U1) (b) Copy and complete the following table: 81 mj 8K mk U₁ UK 0 20 40 60 100

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Chapter2: Productions Possibilities, Opportunity Costs, And Economic Growth
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1. Kamal (K) and Jamal (J) are the only two individuals in an exchange economy consisting of only two goods, namely
100 units of mangoes (m) and 100 units of guavas (g). The utility functions of Kamal and Jamal are represented by
(m.8k)=m*g* and U, (m,,g,)=m*g* respectively. Furthermore, m + m, 100 and gk + g, = 100.
3/4 1/4
UK
(a) Show that the efficient allocation of mangoes and guavas for Jamal is given by the following condition
8₁
9m,
100-g, 100-m,
(Hint: Let Kamal's utility be fixed at U, then solve the Lagrangian L=U, (m,.g,)+2U (m8k)-Ūx1)
(b) Copy and complete the following table:
81 mj &K mk U₁ UK
0
20
40
60
100
(c)Based on the table which combinations of mangoes and guavas for Kamal and Jamal will yield the most equitable
outcome? Say why.
Transcribed Image Text:1. Kamal (K) and Jamal (J) are the only two individuals in an exchange economy consisting of only two goods, namely 100 units of mangoes (m) and 100 units of guavas (g). The utility functions of Kamal and Jamal are represented by (m.8k)=m*g* and U, (m,,g,)=m*g* respectively. Furthermore, m + m, 100 and gk + g, = 100. 3/4 1/4 UK (a) Show that the efficient allocation of mangoes and guavas for Jamal is given by the following condition 8₁ 9m, 100-g, 100-m, (Hint: Let Kamal's utility be fixed at U, then solve the Lagrangian L=U, (m,.g,)+2U (m8k)-Ūx1) (b) Copy and complete the following table: 81 mj &K mk U₁ UK 0 20 40 60 100 (c)Based on the table which combinations of mangoes and guavas for Kamal and Jamal will yield the most equitable outcome? Say why.
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