ASSIGNMENT SOLUTION Case Solution
Question 1
The city improvement recommendation can only be made if the costs are lower than the expected benefits. Based on the waiting time elasticity of demand of -0.6, if the waiting time is reduced by 15 minutes, then the number of trips would increase by 45000 as shown in the excel calculations. This would be weekly figure therefore; we have multiplied it by 52 weeks to get an annual figure of 2340000. It is assumed that the subway travel would be open for 52 weeks and 16 hours per weekend. The total WTP revenues and expenses have been calculated. We have a net profit of $ 651,000 therefore; the city should implement this improvement. The computations are shown below:
SUBWAY IMPROVEMENT | |
Waiting time E(d) | -0.6 |
Trips per year | 7800000 |
E(d) = % change in trips/% change in waiting time | |
% change in waiting time | 50% |
% change in trips | 30% |
New Trips | 2340000 |
Total Trips | 10140000 |
Revenues | |
WTP from new riders | 70200000 |
WTP from existing riders | 23400000 |
Total WTP | 93600000 |
Less: Expenses | |
Capital Stock expenses | 3000000 |
New weekend employee wages | 36608000 |
Tax Driver Wages | 18304000 |
Other new employee wages | 9152000 |
Costs of Subway rides | 27885000 |
Add: Decrease in pollution | $2,000,000 |
Total Expenses | $92,949,000 |
Net benefit/ (cost) | $651,000 |
Question 2
a).
We have used the estimates calculated in column 2 because these have been adjusted for heteroskedasticity. Based on the percentage change in price estimate of -0.24, the new price that should be charged is $ 2.8 per acre per residents. The computations are shown in excel spreadsheet. The developer wants to buy 20 acres of the land from the total of 717.504 acres. The total price that should be charged for these 20 acres should be $ 30270.3 as shown below:
MARKET PRICE TO CHARGE | |
Percentage change in Price | -0.24 |
Residents | 19392 |
Acres of open space per resident | 0.037 |
Total acres of open space | 717.504 |
Acres to buy | 20 |
Change in acres of open space | 697.504 |
Market price per acre per resident | 2.04 |
Market price to charge | 2.8 |
Total market price | 30270.3 |
b).
The above charge is based on the estimates developed by the model; therefore, the charge can be adjusted by lowering it if the developer wants and increasing it if the government wants. The estimate for the price elasticity is again based on a number of assumptions and historical data therefore, adjustments can be made. However, the above charge should be a fair charge as it is based on the estimates generated by the regression model.
Question 3
a).
The total tax that would be collected would be:
$ 154, 500, 000 x 15 cents
Tax Revenues = $ 23175000
b).
The net cost (deadweight loss) of the program to the society would be:
Total Spent on Rolls | 154500000 |
Cost/market price per roll | 1.35 |
Total rolls bought | 114444444 |
Tax increase per roll | 0.15 |
New price | 1.5 |
% change in price | -10% |
E(d) | -0.15 |
% change in demand | 1.50% |
Decrease in Demand | 1716667 |
Deadweight Loss (net cost) | 2317500 |
Question 4
a).
The average life expectancy of the world in years and the standard deviation is as follows:
Mean of Life Expectancy | 72.521 |
Standard Deviation of Life Expectancy | 8.453 |
b).
The unweighted regression of GDP per capital based on Gini, government consumption, debt as a percent of GDP and GDP percent agriculture has been generated in R software and in excels spreadsheet as well. The data has been collected from CIA world Factbook. The data set has been trimmed as we have limited data for GINI index of the world countries. Therefore, the total number of observations of all the variables is 145. The R programming regression output for multiple regression models is shown below:
##
## Call:
## lm(formula = GDP per capita ~ GINI INDEX + public debt as percent of GDP + GDP - % agriculture + Government consumption , family = "binomial",
## data = CIA)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.627 -0.866 -0.639 1.149 2.079
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -32129.045 1800.3244 -3.50 0.0000 ***
## GINI INDEX 825.555 69.0863 2.07 0.0000 *
## public debt as percent of GDP 488.3202 21.2145 2.42 0.0000 *
## GDP - % agriculture 4.5709 24.1930 -3.23 0.8504 *
## Government consumption 51.5134 61.6157 -3.48 0.4046 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 139.98 on 144 degrees of freedom
## Residual deviance: 138.52 on 144 degrees of freedom
## AIC: 400.5
##
## Number of Fisher Scoring iterations: 13
Based on the results of the regression model, we can say that the world GDP per capita is significantly impacted by Gini, government consumption, debt as a percent of GDP and GDP percent agriculture as the p value of the model is 0.000. If we analyze the coefficients of all the independent variables, then we can see that only GINI INDEX and public debt as a percent of GDP have a significantly positive impact on the GDP per capita. Based on the above model, the GDP per capital of China for the next year would be as follows:......................................
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