Suppose consumers use k units of good X and w units of good Y in fixed proportion. Then, which of the following utility function represents this preference? X Y U(X,Y) = min{,. k' O U(X,Y) = kX + wY. O UCX.Y) = min. )U(X,Y) = wX + kY.

1. Jan has the following utility function for broccoli: U(B) = 54B - 0.5B³ a) What is Jan's marginal utility function?

Suppose that a consumer has the utility function U(X,Y)= 2X 1/2 y 1/2 for X>0 and Y> 0. Which of the following utility functions would not represent the same preferences? U(X,Y)= 2(X + Y) 1/2 U(X,Y)=2x1/2y 1/2 - 100 O U(X,Y)= In 2 + InX+ In Y O U(X,Y)= X 1/2 y 1/2 O U(X, Y) = 4XY

Refer to the graph below Quantity of Y 160 0 Multiple Choice The consumer's income is $1,000 Why doesn't the consumer choose the combination at point B O Quantity of X 200 O The marginal utility of Y exceeds the marginal uplity of X O The consumer is willing to give up more X for an additional unit of Y than must be given up given the relative prices of X and Y. The marginal utility per dollar spent on X exceeds the marginal utility per dollar spent on Y The consumer is willing to give up more Y for an additional unt of X than must be given up given the relative prices of X and Y

A B C

2) Which of the following utility functions represent the same preferences? Explain. a) U (x₁, x₂) = X₁ X₂ b) W (x₁, x₂) = 5lnx₁ +5lnx₂ c) V (x₁, x₂) = x₁¹/3x₂ ¹/3 - 0.8 d) Z(x₁, x₂) = 0.5x₁ + 0.5x₂