Cobb-Douglas utility curve

• $u(x,y)=x^a{y}^{1-a}$
• 
  • src
• Figure shows $u(x,y)=x^{0.5}{y}^{0.5}$ when a=0.5
• This is just a weighted average if we take the logarithm of x and y, respectively
  • That is, the effect of one good is proportional to the logarithm of its quantity - law of diminishing marginal utility
• On the other hand, budget constraint is a straight line on this space that does not take logarithms
  • Cobb, C. W., & Douglas, P. H. (1928). A theory of production. The American Economic Review, 18(1), 139-165.

Constant Elasticity of Substitution (CES) utility function

• $u(x,y)=(a{x}^r+b{y}^r{)}^{1/r}$

quadratic

• $u(x,y)=2ax-(b-y{)}^2$

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