detailed answers to each part and graphs

Question 3B For each of the following, indicate whether the relationship is possible or not and explain your answer briefly: (a) A good is normal and its cross-price demand relationship is positive. (b) A good is inferior and its cross-price relationship is negative. (C) Tastes are homothetic and one of the good's cross-price relationship is negative. Now consider specific tastes represented by particular utility functions. (d) Suppose tastes are represented by the function u(11, 12) = a In 21 + x2 What is the 6 shape of the cross-price demand curves for 21 and 22? (e) Suppose instead tastes are Cobb-Douglas. What do cross-price demand curves look like? Question 3C Engel curves plot the relationship between income on y axis and consumption of goods on r axis, leaving everything else constant. (a) If price of relevant good x changes, then for a fixed nominal income, Engel curves will shift. Plot the Engel curves and illustrate shifts in Engel curves for reduction in price of good for each of the three cases when good r is a regular inferior, normal and giffen good respectively. (b) In the Cobb Doughlas case, u = zyl a own price demand functions are r = al and (1-a)! We also know that I y = = 1-0. Derive the income demand curves for T and y which show income as function of u and y respectively and plot these Engel curves for a = = 0.5. Carefully illustrate the slope of these Engel curves. PE Q PX Py Py