A consumer earns I a week and spends his entire weekly income on new dress shirts and ties, because these are the only two items that provide utility to him.

Further- more, he insists that for every shirt he buys, he must also buy a tie (without the
ties, the new shirts are worthless and vice versa). Let Ps and Pt denotes the price
of a shirt and the price of a tie, respectively.

(a) Derive the consumer's demand function for shirts and the demand function for
ties.

(b) Derive the income elasticity of demand for shirts. Are shirts normal goods or
inferior goods for the consumer? Explain.

(c) Derive the cross-price elasticity of demand for shirts with respect to ties. Are
shirts and ties substitutes or complements? Explain.

(d) Suppose that the price of a shirt decreases from P's to P''s.
The price of a tie and the consumer's income remain at Pc and I, respectively. Let bundle A be
the consumer's choice before the price change, and bundle B be the choice after
the price change. Decompose the substitution effect and the income effect, and
explain the result.