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Question: please explain and answer thank you a consumers preferences are...

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Please explain and answer. Thank you!

  1. A consumer’s preferences are represented by: U(x,y) = 2large sqrt{x} + large sqrt{y} , (MUx = large rac{1}{sqrt{x}} , MUy = 2VY )
    Given this utility function, the consumer needs to give up increasing amounts of good X in order to consume additional amounts of good Y and remain as well off.
    a) True (b) False
  2. A consumer’s preferences are represented by: U(x,y) = 2ln(x) + ln(y), (MUx = 2/x, MUy = 1/y)
    Given this utility function, the MRSxy decreases along the indifference curve as X increases.
    (a) True (b) False
  3. Consider the utility function: U(x,y) = x + y + xy, (MUx = y + 1, MUy = x + 1)
    Given this utility function, the marginal utility of good Y increases as Y increases, holding X constant. Or, the same, good Y becomes more and more valuable for consumer as he buys more and more good Y, holding constant consumption of good X.
    (a) True (b) False
  4. A consumer’s preferences are represented by: U(x,y) = x + y + xy, (MUx = y + 1, MUy = x + 1)
    Given this utility function, the assumption that more is better is satisfied for both goods. Or, the same. Both goods are "good" goods.
    (a) True (b) False
  5. An increase in the price of good X and an equal percentage increase in the price of good Y decreases the X-intercept and the Y-intercept, but does not change the slope of the budget line.
    (a) True (b) False
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