Suppose that Madelyn always divides her annual jewelry budget between earrings (good x) and necklaces (good y) such that she always spends 40% of her budget on earrings per year. Furthermore, the current price of a pair of earrings is $10, the current price of a necklace is $15 and her yearly jewelry budget is $320.
a. Write Madelyn’s demand function for earrings and her demand function for necklaces.
b. Draw a price consumption path for Madelyn when the price of necklaces increases from $15 to $20. Be sure to fully label axes and identify intercepts and points on the price consumption path.
c. Calculate Madelyn’s own price elasticity of demand for earrings and interpret what your answer says about Madelyn’s response to price changes in this good.
d. Draw an Engel curve for earrings. Be sure to fully label axes.
e. Determine the cross price elasticity for demand of necklaces with respect to the price of earrings. Are these goods complements, substitutes or unrelated?