Question: Adam's preferences are represented by the utility function (1,2) = 1 2 2 3 . The prices of 1 and 2 are 1 and 2

Adam's preferences are represented by the utility function (1,2) = ₁²₂³. The prices of ₁and ₂ are ₁and ₂, respectively.

a. What is the slope of Adam's indifference curve?

b. If Adam's budget line is tangent to his indifference curve at (1,2), then ₁_{1 /}₂₂=?

c. Solve for the optimal values of _1,₂ that Adam will consume.

d. When he is consuming the best bundle he can afford, what fraction of his income does Douglas spend on ₁?

e. Adam's friends, Malthus and Ricardo, have similar utility functions, but the exponents may be different, or their utilities may be multiplied by a positive constant. If a family member has a utility function (,) = ₁^a₂^b where a, b, and c are positive numbers. What fraction of their income will Adam's friend spend on ₁?

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