As shown in the appendix to chapter4, theCobb-Douglas form of utilityfunction, U(X,Y)= alog(X) +(1-a) log(Y), yields demand functions X= (a/PX)I and Y= [(1-a)/PY]I. These demand functions have some unique properties. One is that thecross-price elasticities arezero, as pointed out in theappendix, because neither demand depends on the price of the other good.

Another unique property is that theown-price elasticities are constant and do not depend on the particular values of the prices and income. Usingcalculus, the price elasticity of demand for good X can be calculated as EP=PX/X * X/PX. Therefore, the price elasticity of demand for good X equals ____ (Enter your response as real number rounded to one decimalplace.)

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 EI=I/X * X/I. The income elasticity of demand for good X is therefore _____(Enter your response as a real number rounded to one decimalplace.)

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 is (a or 1/2 or I/PX)

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