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The utility function for an individual is given by (1, 2 ) = 1 2 , and the budget constraint is 11 + 22 =

The utility function for an individual is given by (1, 2 ) = 1 2 , and the budget constraint is 11 + 22 = .

(i) Derive the marginal rate of substitution (MRS) between 1 and 2. Hence find the MRS when = 1 2 , = 2 3 , = 3 2 .

(ii) Derive expressions for the optimal choices for 1 and 2. Hence calculate the optimal values for 1 and 2 when 1 = 2, 2 = 3, = 39. (The values of A, a and b are already provided in (i) above.)

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