This question explores some features of the Cobb-Douglas utility function by analyzing the general Cobb-Douglas utility function, U (x, y) = x'lyb. Let's assume for this recitation problem set that a + b=1. a. Derive the demand functions for goods x and y. b. As a becomes larger, will the individual consume more or less of good x relative to good y? Note: The answer to this question gives us an intuitive understanding of a. c. Do the demand curves for goods it and y necessarily slope downward? Explain and mathematically justify. d. Graph the price consumption curve (as the price ofx changes). e. Derive the elasticity of demand for good x, the cross-price elasticity of demand for good x with respect to the price of good y, and the income elasticity of demand for good x