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Consider a consumer with preferences represented by the utility function: U(x,y) = 3x + 6 √...

Consider a consumer with preferences represented by the utility function:

U(x,y) = 3x + 6 √ y  

  1. Are these preferences strictly convex?
  2. Derive the marginal rate of substitution
  3. Suppose, the utility function is:

U(x,y) = -x +2 √ y  

  1. Are there any similarities or differences between the two utility functions?
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