Recall That the Cobb-Douglas Utility Function U(X,Y)= XᵃY¹⁻ᵃ Has the Unusual

Essay

Recall that the Cobb-Douglas Utility function U(X,Y)= XᵃY¹⁻ᵃ has the unusual property that the demand for each good depends only on its own price.Therefore,a consumer will always allocate the same proportion of income to each good.Specifically,the demand for X is
X* = aI/pₓ
where I is income and pₓ is the price of X.
a.What is the price elasticity of demand for X?
b.What is the direction of the income effect on X of an increase in pₓ?