Question

A firm derives revenue from two sources: goods X and Y. Annual revenues from good X and Y are $10,000 and $20,000, respectively. If the price elasticity of demand for good X is −2.0 and the cross-price elasticity of demand between Y and X is 1.5, then a 4 percent increase in the price of X will:

Answer 1

Increase the total revenue increases by $400

Step-by-step explanation:

R = PxQx + PyQyce of good X

R = Revenue, Px = Price of good X, Py = Price of good Y, Qx = Quantity of goods X, Qy = Quantity of goods Y.

Now, suppose the price of goods X increases by 4$

ΔR = [PxQx(1+eQxPx) + PyQy*eQyPy] * %ΔPx

= [Rx(1+eQxPx) + Ry*eQxPx] * %ΔPx

= [ 10,000*(1 - 2.0) + 20,000 (1.5)] * 0.02

= -10000 + 30000 * 0.02

= 20,000 * 0.02

= $400

Thus, it means with increase in price of goods X by 4%, the total revenue increases by $400