Recall That the Cobb-Douglas Utility Function U(X,Y)= X^aY^1-A Has the Unusual

question 21

Essay

Recall that the Cobb-Douglas Utility function U(X,Y)= X^aY^1-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/p_x
where I is income and p_x 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 p_x?

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