A firm derives revenue from two sources: goods X and Y. Annual revenues from good X and Y are $10,000 and ... ?

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 - 4.0 and the cross-price elasticity of demand between Y and X is 2.0 then a 2 percent price decrease will

a. Increase total revenues from X and Y by $520

b. Decrease total revenues from X and Y by $520

c. Leave total revenues from X and Y unchanged

d. Decrease total revenues from X and Y by $600

The correct answer is (d) Decrease total revenues from X and Y by $600

Lets first calculate change in revenue due to good X

TR = P*Q

where TR = Total revenue, P = Price and Q = Quantity

Formula:

% change in (A*B) = % change in A + % change in B

Thus % change in TR = % change in (P*Q) = % change in P + % change in Q

Own Price Elasticity of demand of X = % change in quantity of X / % change in Price of X

It is given that, Own Price Elasticity of demand of X = - 4 and % change in Price of X = - 2% (negative sign means that price has decreased)

Hence, - 4 = % change in quantity of X / (-2) = > % change in Quantity of X = 8%.

Here % change in Q = 8% and % change in P = - 2%

% change in (TR) = % change in (P*Q) = % change in (P) + % change in (Q) = - 2 + 8 = 6%

Hence Revenue due to good X increases by 6%.

So change in revenue due to Good X = 6% of 10,000 = (6/100) * 10000 = 600

Now Lets first calculate change in revenue due to good Y

TR = P*Q

where TR = Total revenue, P = Price and Q = Quantity

Formula:

% change in (A*B) = % change in A + % change in B

Thus % change in TR = % change in (P*Q) = % change in P + % change in Q

Cross Price Elasticity of demand between X and Y = % change in quantity of Y / % change in Price of X

It is given that, Cross Price Elasticity of demand between X and Y = 2 and % change in Price of X = - 2% (negative sign means that price has decreased)

Hence, 2 = % change in quantity of Y / (-2) = > % change in quantity of Y = 2 * (-2) = - 4.

Here % change in Q = - 4% and % change in P = - 2%

% change in (TR) of good Y = % change in (P*Q) = % change in (P) + % change in (Q) = - 2 + (-4) = - 6% (negative sign means that TR will decrease)

Hence Revenue due to good Y decreases by 6%.

So change in revenue due to Good Y = - (6% of 20,000) = (6/100) * 10000 = - 1200 (negative sign means that revenue will decrease)

Hence Overall change in total revenue = Change in Revenue due to good X + Change in Revenue due to good Y

=> Overall change in total revenue = 600 + (-1200) = - 600

Hence Overall Revenue will decrease by 600

Hence, the correct answer is (d) Decrease total revenues from X and Y by $600