Suppose Fiberboard Inc. has estimated its log-linear demand function for cardboa
ID: 1137455 • Letter: S
Question
Suppose Fiberboard Inc. has estimated its log-linear demand function for cardboard boxes as: [ln(Boxes)] = 90 – 2.4[ln P] + 1.5[ ln(M)] + 0.3 [ln(Advt)] Where: Boxes is the quantity of boxes P is the own price M is market income Advt is expenditures on advertising And: ln denotes the natural logarithm a. What is the price elasticity of demand? b. Is advertising expenditures elastic? c. Assuming each of these variables is statistically significant, how would the consumption of the boxes change if there is a simultaneous 10% reduction in price, a 5% reduction in income, and a 20% reduction in advertising? Suppose Fiberboard Inc. has estimated its log-linear demand function for cardboard boxes as: [ln(Boxes)] = 90 – 2.4[ln P] + 1.5[ ln(M)] + 0.3 [ln(Advt)] Where: Boxes is the quantity of boxes P is the own price M is market income Advt is expenditures on advertising And: ln denotes the natural logarithm a. What is the price elasticity of demand? b. Is advertising expenditures elastic? c. Assuming each of these variables is statistically significant, how would the consumption of the boxes change if there is a simultaneous 10% reduction in price, a 5% reduction in income, and a 20% reduction in advertising? Suppose Fiberboard Inc. has estimated its log-linear demand function for cardboard boxes as: [ln(Boxes)] = 90 – 2.4[ln P] + 1.5[ ln(M)] + 0.3 [ln(Advt)] Where: Boxes is the quantity of boxes P is the own price M is market income Advt is expenditures on advertising And: ln denotes the natural logarithm a. What is the price elasticity of demand? b. Is advertising expenditures elastic? c. Assuming each of these variables is statistically significant, how would the consumption of the boxes change if there is a simultaneous 10% reduction in price, a 5% reduction in income, and a 20% reduction in advertising? Suppose Fiberboard Inc. has estimated its log-linear demand function for cardboard boxes as: [ln(Boxes)] = 90 – 2.4[ln P] + 1.5[ ln(M)] + 0.3 [ln(Advt)] Where: Boxes is the quantity of boxes P is the own price M is market income Advt is expenditures on advertising And: ln denotes the natural logarithm a. What is the price elasticity of demand? b. Is advertising expenditures elastic? c. Assuming each of these variables is statistically significant, how would the consumption of the boxes change if there is a simultaneous 10% reduction in price, a 5% reduction in income, and a 20% reduction in advertising?Explanation / Answer
ln Boxes = 90 ln e - 2.4 ln P + 1.5 ln M + 0.3 ln Advt
ln Boxes = ln [e90 x M1.5 x Advt0.3 / P2.4]
Number of boxes, N = [e90 x M1.5 x Advt0.3 / P2.4] (Demand function)
After the changes, let new number of boxes be N*.
N* = [e90 x (0.95M)1.5 x (0.8Advt)0.3 / (0.9P)2.4]
N* = N x [(0.95)1.5 x (0.8)0.3 / (0.9)2.4]
N* = N x [0.9259 x 0.9352 / 0.7766]
N* = N x 1.115
N* / N = 1.115
So, consumption has increased by 11.5%.
(1) N = [e90 x M1.5 x Advt0.3 / P2.4]
P2.4 = [e90 x M1.5 x Advt0.3 / N]
P = [e90 x M1.5 x Advt0.3 / N]1/2.4 = [e90 x M1.5 x Advt0.3 / N]0.42
Total revenue, TR = P x N = [e90 x M1.5 x Advt0.3] x N0.58
So, MR = dTR / dN = 0.58 x [e90 x M1.5 x Advt0.3] / N0.42
When N = 3, MR = 0.58 x [e90 x M1.5 x Advt0.3] / (3)0.42 = 0.58 x [e90 x M1.5 x Advt0.3] / 1.59
Exact value of MR can be computed if values of M & Advt are given.
(2) & (3) cannot be answered if Cost function is not given.
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