Suppose you have the following hypothetical demand or sales function

a. The coefficient of PY (price of a related commodity) is positive (+0.4). This means that price of good Y and quantity of good X move in the same direction, that is, an increase in price of good Y will cause the quantity demanded of good X to increase.

b. step one: Determine the value of QX

Q X= 600 - 6PX + 20I +0.4PY

But

PX = $80

PY =$1,300

I = $30

Hence,

Q X = 600 - 6(80) + 20(30) + 0.4(1300) = 1240 units.

Step: Determine price elasticity of demand

PED = (change in Quantity /change in Price) * (Price / Quantity)

But,

change in Quantity /change in Price = -6 (obtained by differentiating QX with respect to P in the equation Q X= 600 - 6PX + 20I +0.4PY

Price (PX) = 80

Quantity (Q) = 1240 units

Hence, PED = (-6) * (80/ 1240) = -0.39

PED = -0.39

Since PED < 1, the demand is inelastic.

c.

Price elasticity of demand (PED) = percentage change in quantity / percentage change in price

But PED = -0.39

percentage change in price = 10%

hence

-0.39 = %change in quantity / 10%

%change in quantity = -0.39 * 10% = -3.9%

The sales will decrease by 3.9%.

Impact on revenue

Revenue before price increase

Revenue = Price * Quantity

But

P = 80

Q = 1240

Hence

Revenue = 80 * 1240 = $99,200

Revenue after price increase

New quantity

(3.9 / 100) *1240 = 48.36

1240 ? 48.36 = 1191.64 units

New price

(10 / 100) * 80 = 8

80 + 8 = $88

Revenue = Price * Quantity

But

P = $88

Q = 1191.64 units

Hence

Revenue = 88 * 1191.64 = $104,864.32

R = $104,864.30

Conclusion: the 10% hike in the price of good X increases revenue by $5,664.30 (104,864.30 - $99,200).