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Homework answers / question archive / Part I: True, False, or Uncertain and WhY: Answer 6 of 8 Cubing (raising to the third power) the following utility function will make the MRS at least twice as large: U(x1, x2) = xa1xb2     a, b > 1 The utility function in equation (1) contains no essential goods

Part I: True, False, or Uncertain and WhY: Answer 6 of 8 Cubing (raising to the third power) the following utility function will make the MRS at least twice as large: U(x1, x2) = xa1xb2     a, b > 1 The utility function in equation (1) contains no essential goods

Economics

Part I: True, False, or Uncertain and WhY: Answer 6 of 8

  1. Cubing (raising to the third power) the following utility function will make the MRS at least twice as large:

U(x1, x2) = xa1xb2     a, b > 1

  1. The utility function in equation (1) contains no essential goods.
  2. A convex choice set will produce more than one optimal bundle for the utility function in equation (1).
  3. Consider the following news report:

From 1945 to 1957, real per-capita incomes rose 29%, yet per-capita household consumption of clothing was unchanged. The introduction of synthetic fibers, in the meantime, reduced the price of clothing by 14% relative to other goods.

Assuming the above facts are correct, it follows that Clothing was an inferior good (for most households) at the time.

  1. In response to a relative price change, the substitution effect for perfect complements overwhelms the income effect.
  2. For a bundle A = xA1, xA2 in a consumer’s choice set, the following obtains:

                                MUx1/MUx2 < p1/p2

This consumer would be better off consuming a bundle with more x2 and less x1 than his or her current bundle.

  1. Write a Lagrange function to maximize the area of a rectangle (A = l·w) when the perimeter of the rectangle must be 50 (P = 2l +2w).
  2. Supposing there is only one good in the world (x), which is denominated in p and purchased with a numeraire comprising I, the income elasticity of x must be 1 and its own-price elasticity (−)1.

Part II: Short Answer: Answer 2 of 3

  1. A friend of yours receives an unexpected inheritance from a distant relative. Knowing you’re a student of economics, he asks you what to do with it. He is not only concerned about the Return on his investments but also the Risk; he prefers to have less risk and higher returns.
    1. With Risk on the horizontal axis and Return on the vertical axis, indicate the direction of your friend’s preferences and plot some point, A, that corresponds to an investment (bundle) that has stable and predictable returns.
    2. Now plot another bundle, B, that represents a different investment that is riskier but that your friend would find equally attractive to A. What must be true about the values of Risk and Return for this investment (bundle) compared to A?
    3. If your friend’s tastes for Risk and Return are convex, he should diversify (i.e., get some of many investments, rather than all of one).
  2. Consider the graphic below. Indicate in which Figure(s) you find the following to be true:

 

 

    1. X is normal. (b) Y is inferior.

(c) X is a Giffen good.

  1. Since 1900, real incomes have increased dramatically while the average number of Children per family has decreased. Model each of the following candidate explanations for these observed phenomena using budget lines and indifference curves between Children (per family) on the horizontal axis and AOG on the vertical. Be sure to account for both the real income change and the overall number of Children (per family).
    1. Children are an inferior good.
    2. Children are a normal good, but the price of Children has risen relative to AOG.
    3. Tastes have changed such that families wish to have fewer Children.

 

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