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M8. The demand function for good 1 is given by q1 = Appzy' where p, is the price of good 1, p2 is the price of good 2, and y is income: a) Take the natural logarithm of the both sides of the demand function. Find the partial derivatives of the logarithmic transformation with respect to P1, P2 and y (i.e. find dlnq1 dlnq1 and dinq1 ). dlnp1 dinp2 dlny b) Show that the partial derivatives of the logarithmic transformation are equal to the corresponding partial elasticities of the original function (the own-price elasticity, the cross-price elasticity and the income elasticity). c) Are good 1 and good 2 substitutes or complements