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 z? ​​​​​ ______________ 4) are x and z substitutes or complements? ​​​​​​ ______________ 5) what is the income elasticity for x? ​​​​​​​ ______________ 6) if incomes increased by $ 5,000, what would be the increase in sales of x?

Answer 1

Qx=1000-5Px-10Py+9Pz+0.001i

Sales = Qx=1000-5*10-10*4+9*10+0.001*20000= 1020

Elasticity of demand (Ed) = dQ/dPx*Px/Q = -5*10/1020 = -0.049

Cross Elasticity between X and Z= dQx/dPz*Pz/Qx = 9*10/1020 = 0.088

The goods X and Z are substitutes as the cross elasticity between them is positive.

Income Elasticity = dQx/di*i/Qx = 0.001*20000/1020 = 0.02

The good is considered as normal good as the income elasticity is positive.

Income Elasticity = % Change in Qty demanded/% Change in income

% change in income = (25000/20000-1)*100 = 25%

0.02 = % Change in qty/25

% Change in qty = 25*0.02 = 0.5

The sales will increase by 0.5.