In: Economics
John thinks that the only way to consume hotdogs, denoted by H, and buns, denoted by B, are together in equal proportions. Hotdogs and buns cost Ph and Pb , respectively, and John has m dollars to spend on the two goods. All this means that John's demand function for hotdogs looks as follows: H= (m/Ph+Pb). The price of a hotdog is twice as high as the price of a bun.
a) Derive the price elasticity of John's demand for hotdogs. Is his demand elastic, inelastic, or unit-elastic?
b) Derive the cross-price elasticity of John's demand for hotdogs with respect to the price of a bun. Are hotdogs a gross substitute or a gross complement of buns?
c) Derive the income elasticity of John's demand for hotdogs. Are hotdogs a normal or an inferior good for John? If it is normal, is it a luxury or a necessity?