Managerial Economics: Analysis of Bus Mile Driven, Marginal Productivity, Elasticity, Optimal Combination, and Break-Even Analysis

MANAGERIAL ECONOMICS
QUESTION A
PART A
The Number of Bus Mile driven determined on the basis of data provided stands at 15930.9 Miles
whereby ln 200 stands at 5.29, ln 400 stands at 5.99 and ln 4000 stands at 8.29;
PART B
The Marginal Product of Labour, Capital and Gasoline stands at 31.814, 23.884 and 0.79 respectively
based on increasing the value of input by one and testing the change in output based on the same.
Yes, all the three of them are positive as calculated in Excel annexed to this note.
Yes, the addition to output by increase in input decreases a more and more input is added to
production on account of diminishing marginal productivity. This happens on account of utilisation of
asset resulting in lower output compared to previous input increase. Thus, the diminishing marginal
productivity results in lower marginal product as more and more unit are added.
PART C
The output elasticity has been computed in Excel by using the formula of Change in Quantity/
Quantity Multiplied by Input divided by change in input.
On the basis of above stated formula, the Elasticity has been computed at 0.3 for Capital, 0.59 for
Labour and 0.19 for Gasoline.
Refer Excel for detailed computation.
PART D
On increasing the input by 10% , the output increases by 12.1% as depicted in excel. Thus, the same
depicts an increasing return to scale. Further, if the Cobb-Douglas model is re written in Power
function and the Coefficients are added it shall add up to 1.2 which exhibits an increasing return to
scale which is contrary to the constant return to scale assumed under the model.
Refer Excel for detailed computation.
PART E
The firm is using the optimal combination of labour, capital and gasoline as MPK/Price of
K=MPL/Price of L=MPG/price of G are same.
Further, the price that should be charged to maximise profit stands at $33.65
PART F
For determining the statistical significance at 5% level, one needs to look at t statistic of the
parameters which stands at 3.40 for K , 4.15 for and 3.05 for G. Further, the value of t at 5%
significance stands for 24-3-1 observation = 20 degrees of freedom is 2.086. Thus, the production
function is statistically significant at 5% level of confidence.
94% of the variation in Q is explained by the regression as the same is indicated by R 2. The formula
for the same is Explained Variation/ Total Variation.