Question

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

6. Calculate the point income elasticity of demand, given that I = $170,000 and that PS = $8500 (thus QS should equal 121,600). Other variables are as given at the top before #1. Does this elasticity indicate that the demand for Smooth Sailing boats is relatively responsive to changes in income? Explain why or why not. The formula is:

Answer 1

6)

Qs = 89830 - 40PS + 20PX + 15PY + 2I +.001A + 10W

Substituting the values

Qs = 89830 - 40(8500) + 20(9500) + 15(10000) + 2(15000) +.001(170000) + 10(160)

     = 89830 - 340,000 + 190,000 + 150,000 + 30,000 + 170 + 1600

     = 121,600

Here, I = 15,000          [Note: i think you have wrongly written I = 170000]

Point income elasticity of demand = (∆Q/∆I) * I / Q              [Where, ∆Q/∆I is weather coefficient in the demand function]

                                                        = 10 * (15000 / 121,600)

                                                        = 1.23

Since income elasticity is greater than 1, this elasticity indicate that the demand for Smooth Sailing’s boats is relatively responsive to changes in income.