Answer:
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
Explanation:
