Answer:
(a) To calculate the price elasticity of demand for free-night calls, we use the formula:
E_p = (% change in Q) / (% change in P) * (P / Q)
We are given that P = GHC 0.50 and Q = 4000 - 2.25(0.50) + 10.52(10) + 40(100) - 0.10 + 100(120) = 7587.5
To calculate the percentage change in quantity demanded, we need to use the midpoint formula:
% change in Q = [(new Q - old Q) / ((new Q + old Q) / 2)] * 100
Assuming a 10% decrease in price, the new price would be GHC 0.45:
% change in Q = [(Q at GHC 0.45 - Q at GHC 0.50) / ((Q at GHC 0.45 + Q at GHC 0.50) / 2)] * 100
% change in Q = [(4000 - 2.25(0.45) + 10.52(10) + 40(100) - 0.10 + 100(120) - 7587.5) / ((4000 - 2.25(0.45) + 10.52(10) + 40(100) - 0.10 + 100(120) + 7587.5) / 2)] * 100
% change in Q = -4.46%
Plugging in the values, we get:
E_p = (-4.46%) / (-10%) * (GHC 0.50 / 7587.5)
E_p = 0.023
The price elasticity of demand for free-night calls is 0.023, which means that demand is inelastic. This suggests that a 10% decrease in price would result in a less than 10% increase in quantity demanded.
(b) To calculate the cross-price elasticity of demand between free-night calls and family and friends, we use the formula:
E_xy = (% change in Q_x) / (% change in P_y) * (P_y / Q_x)
Assuming a 10% increase in the price of family and friends, we get:
% change in Q_x = [(new Q_x - old Q_x) / ((new Q_x + old Q_x) / 2)] * 100
% change in Q_x = [(4000 - 2.25(0.50) + 10.52(10) + 40(100) - 0.10 + 100(120)) - (4000 - 2.25(0.50) + 10.52(10) + 40(110) - 0.10 + 100(120))] / ((4000 - 2.25(0.50) + 10.52(10) + 40(100) - 0.10 + 100(120)) + (4000 - 2.25(0.50) + 10.52(10) + 40(110) - 0.10 + 100(120))) / 2] * 100
% change in Q_x = -2.14%
Plugging in the values, we get:
E_xy = (-2.14%) / (10%) * (GHC 100 / 7587.5)
E_xy = 0.28
The cross-price elasticity of demand between free-night calls and family and friends is 0.28, which means that they are slightly complementary goods.
(c) To maximize revenue, MTN should set the price of free-night calls at a level where the marginal revenue equals marginal cost. The marginal revenue can be calculated by taking the derivative of the demand function with respect to price and setting it equal to zero:
MR = 4000 - 4.5P + 10.52C + 40X - W + 100M = 0
Solving for P, we get:
P = (4000 + 10.52C + 40X - W + 100M)/4.5
Substituting the given values of C, X, W, and M, we get:
P = (4000 + 1052 + 4000 - 0.10 + 12000)/4.5
P = GHC 5,000
Therefore, MTN should set the price of free-night calls at GHC 5.00 to maximize revenue.
(d) With the prices of all products doubled and income levels of clients remaining unchanged, the demand function becomes:
Q = 4000 - 4.5P + 10.52C + 40X - W + 100M
Using the same method as in part (a), we can calculate the new price elasticity of demand to be -1.682, which is still inelastic.
Using the new demand function, the optimal price to maximize revenue becomes:
MR = 4000 - 9P + 10.52C + 40X - W + 100M = 0
Solving for P, we get:
P = (4000 + 10.52C + 40X - W + 100M)/9
Substituting the given values of C, X, W, and M, we get:
P = (4000 + 1052 + 4000 - 0.10 + 12000)/9
P = GHC 2,000
Therefore, MTN should set the price of free-night calls at GHC 2.00 with the new prices to maximize revenue.
(e) Accountants are likely to overstate profits as compared to economists because they use historical cost accounting, which values assets and liabilities at their original purchase price. This method does not take into account the changes in the value of assets and liabilities due to inflation, changes in market conditions, or other economic factors. As a result, the reported profits may not accurately reflect the true economic value of the company's assets and liabilities. In contrast, economists use market value accounting, which values assets and liabilities at their current market value, taking into account changes in economic conditions.