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Determine whether or not the following utility functions represent "Strictly Convex" preferences. Justify your answers very clearly and show how the indifference curve associated with each utility function looks like.
a) U(x1, x2) = ln(x14x21/2+3)

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Namita kumari
Namita kumariLv6
28 Sep 2019

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Related questions

An Individual consumes good X1 and X2. Let W be the wealth of the individual and P1>0, P2>0 be the prices of the goods. For each of the utility functions provide a real life example of two goods X1 and X2 that satisfy them, draw the indifference curves, determine whether preferences are convex, strictly convex or neither, and compute the Walrasian demand, indirect utility function, Hicksian demand, and Expenditure function.

  1. U (X1, X2) =(X1^0.4) *(X^0.6)
  2. U (X1, X2) =min (X1, X2) +3 max (X1, X2)

Determine whether or not the following pairs of utility functions are monotonic transformations of each other. Justify your answers by calculating the MRS of each function.
a) U1(x1, x2) = min{x1/2,6x2} and U2(x1, x2) = max{x1/2,6x2}

A. True, False, Uncertain and Explain: determine whether the statement is true, false or uncertain and explain your reasoning – you only earn points for your explanation. 1. If preferences are convex, the set of points at least as good as any given point is a convex set. 2. If preferences are strictly convex, the set of points “no better than” any given point is a convex set. 3. If a consumer has strictly convex preferences over two goods and she is indifferent between bundle A given by (4, 6) and bundle B given by (2, 8), then she prefers bundle C given by (3, 7) over either bundle A or bundle B. 4. If a consumer has preferences over two "bads" then these preferences cannot be convex. 5. If apples (a good) are on the horizontal axis and dirty socks (a bad) are on the vertical axis then the indifference curves that represent convex preferences over these two items is upward sloping and flattens out as moving from left to right. 6. If preferences are not monotonic then they cannot be transitive

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