You are the manager of a firm that receives revenues of $50,000 per year from pr
ID: 1132541 • Letter: Y
Question
You are the manager of a firm that receives revenues of $50,000 per year from product X and $90,000 per year from product Y. The own price elasticity of demand for product X is -3, and the cross-price elasticity of demand between product Y and X is 1.6. How much will your firm's total revenues (revenues from both products) change if you increase the price of good X by 2 percent? Please provide a dollar amount.
Instructions: Round your answer to the nearest dollar. Include a minus (-) sign if applicable.
$ __________
Explanation / Answer
Revenue from product X (TRx) = Px.Qx = $50,000
Reveneue from product Y (TRy) = Py.Qy = $90,000
Total revenue (TR) = TRx + TRy = $(50,000 + 90,000) = $140,000
Own-price elasticity of demand = % Change in quantity demanded / % Change in price
-3 = % Change in quantity demanded / 2%
% Change in quantity demanded = 2% x (-3) = -6% (Decrease)
Therefore, Px becomes (1.02Px) and Qx becomes (0.94Qx).
New total revenue from X (TRx1) = (1.02Px) x (0.94Qx) = (1.02 x 0.94) x (Px.Qx) = 0.9588 x $50,000
= $47,940
Cross-price elasticity of demand = % Change in demand for Y / % Change in price of X
1.6 = % Change in demand for Y / 2%
% Change in demand for Y = 2% x 1.6 = 3.2% (Increase)
Therefore, Py remains unchanged and Qy becomes (1.032Qy).
New total revenue from Y (TRy1) = (Py) x (1.032Qy) = 1.032 x (Py.Qy) = 1.032 x $90,000
= $92,880
New Total revenue (TR1) = TRx1 + TRy1 = $(47,940 + 92,880) = $140,820
Change in total revenue = TR1 - TR = $(140,820 - 140,000) = $820
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