#546 Smooth Sailing Inc has estimated the demand function

Smooth Sailing Inc has estimated the demand function - Electrical Engineering

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Free Chegg Question

Smooth Sailing, Inc., has estimated the demand function for its sailboats (quantity purchased annually) as follows:      

Qd= 89,830 - 40ps + 20px + 15Py + 2i + 0.001A + 10w                                                                                                  

Where,

Q_D = quantity purchased,

P_S = the price of smooth sailing sailboats,

P_X = the price of Company X’s sailboat,

P_Y = the price of Company Y’s motorboat,

I = per capita income in dollars,

A = dollars spent on advertising, and

W = number of favorable days of weather in the southern region of the United States.

1. Suppose that P_S = $9,000, P_X = $9,500, P_Y = $10,000, I = $15,000, A = $170,000, and W = 160. Find the price elasticity of demand at that point.
2. Is ∈D elastic, inelastic, or unitary elastic in part (a)? Justify?

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Free Chegg Answer

(a)

The demand function of the Smooth Sailing's sailboats is as follows -

Qd = 89,830 - 40Ps + 20Px + 15Py + 2I + 0.001A + 10w

Ps = 9,000

Px = 9,500

Py = 10,000

I = 15,000

A = 170,000

W = 160

So,

Qd = 89,380 - [40 * 9,000] + [20 * 9,500] + [15 * 10,000] + [2 * 15,000] + [0.001 * 170,000] + [10 * 160]

Qd = 89,380 - 360,000 + 190,000 + 150,000 + 30,000 + 170 + 1600

Qd = 101,150

So,

When the price of the sailboats (Ps) is 9,000 per sailboat, its quantity demanded (Qd) is 101,150 sailboats.

Calculate the  -

 = d(Qd)/dPs = d(89,830 - 40Ps + 20Px + 15Py + 2I + 0.001A + 10w)/dPs = -40

Calculate the price elasticity of demand -

Thus,

The price elasticity of demand at that point is -3.56

(b)

The value of the price elasticity of demand is greater than 1.

When the value of the price elasticity of demand is greater than 1 then the demand is said to be elastic.

Thus,

is elastic.