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 _{11 / 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?