Optimization. 1) (10 points) Assume that the following information on car mileag

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Optimization. 1) (10 points) Assume that the following information on car mileage at various speeds is an accurate depiction of the motor vehicle fleet here in Pennsylvania Gas Consumption Speed Limit (mile/hour) (mile/gallon) 40 38 36 34 32 30 28 45 50 60 65 70 75 The current price of gasoline in Pennsylvania in $3.00/gallon. The average wage is $5.00/hour. Finally, assume that the average driver will be on the road for 500 miles per month, irrespective of the speed limit. Although safety is an important concern, please focus only on the information given to you here in answering the following questions. a) (2 points) Please define the economic decision rule and state how it might help inform the Department of Transportation in setting speed limits in Pennsylvania (4 points) Is the optimal speed limit greater than 65 mph? Why? (2 points) Assume that a new gas tax is imposed such that the price of gasoline increases to $4.50/gallon. How would your answer to (b) change? Why? (2 points) If the gas price is $3.00/gallon, how would your answer to (b) change if the wage increased to $15/hour? Why? b) c) d)

Explanation / Answer

a) Economic decision rule states that if the marginal benefit of an action is higher than the marginal cost, then one should undertake the action; however if the marginal cost is higher than the marginal benefit of the action, one should not undertake it.

Department of transportation can use the economic decision rule to decide speed limit which would be most economical.

b) Calculation of optimal speed:

We would require cost of gas and cost of wages at each speed limit which has been calculated as follows:

Cost of gas = Km driven / gas consumption per mile * rate per gallon

Wages = Km driven / Speed * Rate per hour

The table will be as follows

Speed limit   Gas cons   Cost of gas   Labour
(mile/ hour)   (mile/ gallon)   (in $)   (in $)
45   40   37.50   55.56
50   38   39.47   50.00
55   36   41.67   45.45
60   34   44.12   41.67
65   32   46.88   38.46
70   30   50.00   35.71
75   28   53.57   33.33
Therefore marginal cost and marginal benefit are calculated:

Speed limit   Cost of gas   Marginal cost   Labour   Marginal benefit
45   37.50   -     55.56   -
50   39.47   1.97   50.00   5.56
55   41.67   2.19   45.45   4.55
60   44.12   2.45   41.67   3.79
65   46.88   2.76   38.46   3.21
70   50.00   3.13   35.71   2.75
75   53.57   3.57   33.33   2.38
It can be seen that at speed 70, the marginal cost is greater than the marginal benefit, therefore, the optimal speed would be 65 miles per hour.

c) If gas price increases to $4.50 / gallon:

In this case, the revised calculation will be as under:

Speed limit   Cost of gas   Marginal cost   Labour   Marginal benefit
45   56.25   -     55.56   -
50   59.21   2.96   50.00   5.56
55   62.50   3.29   45.45   4.55
60   66.18   3.68   41.67   3.79
65   70.31   4.14   38.46   3.21
70   75.00   4.69   35.71   2.75
75   80.36   5.36   33.33   2.38
The marginal benefit turns lesser than marginal cost at the speed of 65, therefore the optimal speed is 60 mile/hour.

d) If wage increases to $15/hour :

The revised table will be as follows:

Speed limit   Cost of gas   Marginal cost   Labour   Marginal benefit
45   37.50   -     166.67   -
50   39.47   1.97   150.00   16.67
55   41.67   2.19   136.36   13.64
60   44.12   2.45   125.00   11.36
65   46.88   2.76   115.38   9.62
70   50.00   3.13   107.14   8.24
75   53.57   3.57   100.00   7.14
Therefore the optimal speed limit would be 75 miles per hour.
Thank you.....

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