Question

Suppose using household information we are able to estimate the following demand function:

Q_x = 60- 5P_x + 2.4 P_y - 4P_z + 10I

where Qx = is the quantity of rain coats demanded during a one-year period measured in thousands of units, P_x = the price of a rain coat, P_y= price of a jacket, P_z represents the price of an umbrella, and I is the average annual income of prospective buyers, measured in thousands of dollars.

a) Further, based on current information:, P_x = $60, P_y= $50, P_z = $20, and I = $40.

b) Use the given values of non-price variables (above) to calculate the following demand equation for raincoat.

Q_x = A + β₁P_x.

Where A represents the sum of all the terms on the right-hand side of the equation except raincoat price and β₁ represent the rate of change in demand as price changes (coefficient of P_x).

3. Income elasticity

   Use the Point elasticity formula: ε_I = (ΔQ_d/ΔI) (I/Q_d) to calculate the income elasticity;

   ε_I =

4. Cross price elasticity

Use the Point elasticity formulas: ε_xy = (ΔQ_x /ΔP_y) (P_y/Q_x) and ε_xz= (ΔQ_x /ΔP_z) (P_z/Q_x) to calculate the cross price elasticity for jacket and umbrella:

   ε_xy =

ε_xz=

Only do question 3 and 4.

Answer 1

Question 3

Demand equation is as follows -

Qx = 60 - 5Px + 2.4Py - 4Pz + 10I

Qx = 60 - (5*60) + (2.4*50) - (4*20) + (10*40)

Qx = 60 - 300 + 120 - 80 + 400

Qx = 200

So, when

I = $400

Qd = 200

Calculate ∆Qd/∆I -

∆Qd/∆I = dQx/dI = d(60 - 5Px + 2.4Py - 4Pz + 10I)/dI = 10

calculate the income elasticity -

Ei = (∆Qd/∆I) * (I/Qd)

Ei = 10 * (40/200)

Ei = 2

The income elasticity is 2.

Question 4

(a)

Demand equation is as follows -

Qx = 60 - 5Px + 2.4Py - 4Pz + 10I

Qx = 60 - (5*60) + (2.4*50) - (4*20) + (10*40)

Qx = 60 - 300 + 120 - 80 + 400

Qx = 200

So, when

Py = $50

Qd = 200

Calculate ∆Qd/∆Py -

∆Qd/∆Py = dQx/dPy = d(60 - 5Px + 2.4Py - 4Pz + 10I)/dPy = 2.4

calculate the cross elasticity of demand between raincoats and jackets -

Exy = (∆Qd/∆Py) * (Py/Qd)

Exy = 2.4 * (50/200)

Exy = 0.6

The cross elasticity of demand between raincoats and jackets is 0.6

(b)

Demand equation is as follows -

Qx = 60 - 5Px + 2.4Py - 4Pz + 10I

Qx = 60 - (5*60) + (2.4*50) - (4*20) + (10*40)

Qx = 60 - 300 + 120 - 80 + 400

Qx = 200

So, when

Pz = $20

Qd = 200

Calculate ∆Qd/∆Pz -

∆Qd/∆Pz = dQx/dPz = d(60 - 5Px + 2.4Py - 4Pz + 10I)/dPz = -4

calculate the cross elasticity of demand between raincoats and umbrella -

Exz = (∆Qd/∆Pz) * (Pz/Qd)

Exz = -4 * (20/200)

Exz = -0.4

The cross elasticity of demand between raincoats and umbrella is -0.4