Question

The demand function for your brand X shirts is estimated as Qd x = 1,000 - 5 Px - 10 Py + 9 PZ+ 0 .001 I The price of X is $ 10, Y is $ 4, Z is $ 10 and incomes are $ 20,000.

1) What are your sales? ______________ 2) What is the elasticity of demand for X? _______________ 3) What is the cross elasticity between X and Y? ______________ 4) Are X and Y substitutes or complements? ______________ 5) What is the income elasticity for X? ______________ 6) If incomes increased by $10,000, what would be the increase in sales of X? ______________

Answer 1

Qdx = 1000 - 5Px - 10Py + 9Pz + 0.001*I

1) plugging all values give

Sales = Qdx = 1000 - 5*10 - 10*4 + 9*10 + 0.001*20000

Qdx = 1000 - 50 - 40 + 90 + 20

Qdx = Sales = $1,020

2)

From the demand equation, we have

dQdx/dPx = -5

Elasticity of Demand for X = (dQdx/dPx)*(Px/Qdx)

= (-5)*(10 / 1020)

= -0.05

3)

Cross elasticity between X and Y = (dQdx/dPy)*(Py/Qdx)

= (-10)*(4/1020)

= -0.039

4)

If we see the demand equation, then the coefficient of Py is negative. Increase in the price of good Y reduces the demand for good X. Both X and Y have to be consumed together So, both X and Y are complements of each other.

5)

Income elasticity for X = (dQdx/dI)*(I/Qdx)

= (0.001)*(20000/1020)

= 0.02

6)

New Sales = Qdx = 1000 - 5*10 - 10*4 + 9*10 + 0.001*30000

Qdx = 1000 - 50 - 40 + 90 + 30

Qdx = 1030

Increase in sales of X = 1030 - 1020 = $10