As shown in the appendix to chapter 4, the Cobb-Douglas form of utility function
ID: 1152132 • Letter: A
Question
As shown in the appendix to chapter 4, the Cobb-Douglas form of utility function, U(X,Y) = a log(X) + (1-a) log(Y), yields demand functions X = (a/Px) and Y = [(1-a/PY). These demand functions have some unique properties. One is that the cross-price elasticities are zero, as pointed out in the appendix, because neither demand depends on the price of the other good. Another unique property is that the own-price elasticities are constant and do not depend on the particular values of the prices and income. Using calculus, the price elasticity of demand for Px ax good X can be calculated as Ep = das EpX PX D. Therefore, the price elasticity of demand for good X equals . (Enter your response as real number rounded to one decimal place.) I The income elasticity of demand also does not depend on the values of prices and income. The income elasticity of demand for good X can be calculated as E = The income elasticity of demand for good X is therefore . (Enter your response as a real number rounded to one decimal place.) One other unusual property of these demand functions is that the consumer spends a fixed proportion of income on each good regardless of the values of the prices and income. The fraction of income spent on good X isExplanation / Answer
1. price elasticity of good x is a (Alpha)
2. dX/dI= a/Px
x= a*I/ Px
Income elasticity = I/X * dX/dI
= I/X *a/ Px = (I*a)/( Px *X)
= I*a*Px / a*I*Px = 1
3. Share if income equals the coefficient of the good. In this case it will be alpha or a
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