In: Economics
All questions utilize the multivariate demand function for Smooth Sailing sailboats in C6 on text page 83, initially with: PX = $9500 PY = $10000 I = $15000 A = $170000 W = 160 This function is: Qs = 89830 -40PS +20PX +15PY +2I +.001A +10W
5. Calculate the point weather elasticity of demand with W = 160. Use Qs corresponding to Ps = 9000. Other variables and their values are as given at the top, before question #1. Does this elasticity indicate that the demand for Smooth Sailing’s boats is relatively responsive to changes in the number of favorable weather days? Explain why or why not. The formula is:
5)
Qs = 89830 - 40PS + 20PX + 15PY + 2I +.001A + 10W
Substituting the values
Qs = 89830 - 40(9000) + 20(9500) + 15(10000) + 2(15000) +.001(170000) + 10(160)
= 89830 - 360,000 + 190,000 + 150,000 + 30,000 + 170 + 1600
= 101,600
Point weather elasticity of demand = (∆Q/∆W) * W / Q [Where, ∆Q/∆W is weather coefficient in the demand function]
= 10 * (160 / 101,600)
= 0.016
Since elasticity is less than 1, this elasticity does not indicate that the demand for Smooth Sailing’s boats is relatively responsive to changes in the number of favorable weather days.