Suppose your friend Macklemore derives utility only from purchasing clothing and food. His utility curve is given by:
U(F;C) = 3C + 2CF
where food is denoted by F and clothing is denoted by C. Further suppose that Macklemore only has $20 in his pocket, so that is most amount of money he can spend.
(a) Derive Macklemore's demand for clothing.
(b) What is Macklemore's own-price elasticity of clothing? If the price of clothing is $5 and the price of food is $1, is the demand for clothing
elastic, inelastic, or unit elastic? Is the demand isoelastic?
(c) Is clothing a normal or inferior good for Macklemore? Explain.
(d) ( Initially Macklemore shops at an "expensive" clothing store, where he must spend $5 for each article of clothing. Food costs $1 per item. Graph Macklemore's original budget line with clothing on the horizontal axis.
(e) Using the demand curve derived in part (a) and the prices listed in part (d), what is the utility maximizing amount of clothing that Macklemore will consume? Note: It is okay if this is not a whole number.
(f) Tired of spending so much on clothing, Macklemore begins to shop at a thrift shop, where he "pops some tags" and is able to find clothing for as little as $2 a piece. On the graph in part (d), draw Macklemore's new budget line.
(g)Will Macklemore's utility level, facing cheaper clothing, be lower, the same, or higher? Explain.
(h)With the price of clothing being $2 and the price of food being $1, what is the utility maximizing amount of clothing that Macklemore will
consume? Note: It is okay if this is not a whole number