Douglas Cornfield’s preferences are represented by the utility function u(x₁, x₂)

The prices of x1 and x2 are p1 and p2.

(a) The slope of Cornfield’s indifference curve at the point (x₁, x₂) is _____________.

(b) If Cornfield’s budget line is tangent to his indifference curve at (x₁, x₂), then p₁x₁ p₂x₂ _________. When he is consuming the best bundle he can afford, what fraction of his income does Douglas spend on x₁? ________.

(c) Other members of Doug’s family 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 U(x, y) = cxa₁ xb 2 where a, b, and c are positive numbers, what fraction of his or her income will that family member spend on x₁? _________.

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= a3.