Problem on cross-price elasticity

Question

Kathy purchases two goods, t-shirts and caps.  Her demand for t-shirts is:

Q_t = 44 – 3P_t - P_c + .04I

The price of caps is P_c = $2. And her income is I = $300.

a. Graph a demand curve for Kathy’s t-shirts.

b. Determine the number of t-shirts will Kathy buy if the price of t-shirts is Pt = $5?

c. Determine the number of caps will she buy at such prices and her present income? 

d. An increase in the price of caps will outcome in (circle one):

• Kathy’s demand for t-shirts will shift out away from the origin
• Kathy’s demand for t-shirts will shift in towards the origin
• Kathy will move down along her demand curve for t-shirts
• Can’t tell; it depends on whether or not caps are a normal good to Kathy

e.Determine the cross-price elasticity of the demand for t-shirts with respect to the price of caps?

f. Are caps and t-shirts complements or substitutes? And how do you know?