2. A firm\'s demand function for product X has the following equation: Cr = 1420
ID: 1136919 • Letter: 2
Question
2. A firm's demand function for product X has the following equation: Cr = 1420-20Py-10Py + 0.02M+ 0.04A where Qx is the quantity purchased, Px is the price of X, Py is the price charged for a related good Y, M is per capita income, and A is the dollar spent on advertising. Suppose the firm spends $1200 on advertising, that Py $40 and that income is $8,000 per capita (a) Write the equation of the demand curve for product X. (b) Briefly explain how product X is related to product Y. (Is Y a substitute or a complement, and how can you tell?) (c) Given the stated values of the other independent variables, calculate the point price elasticity of demand for X at Px $50. (d) Given the stated values of M, A, and Py at what price and quantity demanded will total revenue maximized? What will the maximum revenue be?Explanation / Answer
a..)
Qx = 1420 – 20Px – 10(Py) + 0.02M + 0.04A
Substituting values:
Qx = 1420 – 20Px – 10(40) + 0.02(8000) + 0.04(1200)
Qx= 1420 – 20Px – 400 + 160 + 48
Qx= 1,228 – 20Px
b)
Negative sign indicates that both products are complementary. Increase in price of good Y leads to fall in demand for good X.
c)
Qx = 1228 – 20 (50)
= 1228 – 1,000
= 228
Ed = dq/dp * P/Q
= -20 * 50/228
= - 4.3
d)
Q = 1228 – 20P
P= 1228/20 – Q/20
= 61.4 – 0.05Q
TR = P*Q
= 61.4Q – 0.05Q^2
MR on differentiating TR
MR = 61.4 – 0.1Q
61.4 – 0.1Q = 0
Q = 61.4/0.1
= 614
Revenue maximizing quantity is 614
TR or maximum Revenue ;
= 61.4 (614) – 0.05(614)^2
= $ 18,849.8
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