9. Consider the following Cobb- Douglas production function for the bus transpor

Question

9. Consider the following Cobb- Douglas production function for the bus transportation system in a particular city: Q= ?L ^?1 F^?2 K^?3. Where L is the labor input in worker hours; F is the fuel input in gallons; K is the capital input in number of buses; and Q is the output measured in millions of bus miles. Suppose that the parameters (?1, ?2, ?3) of this model were estimated using annual data for the past 25 years. The following results were obtained: ?= 0.0012; ?1= 0.45; ?2= 0.20; ?3= 0.30 d. What type of returns to scale appears to characterize this bus transportation system?

Explanation / Answer

There exists a constant return to scale in this model function. this can be proved as follow. The model give us a view that if: one unit of L increases it will give increase in Q = 0.001% working in table: ? ?1 L factor in on Q ?*L^?1 0.0012 0.45 4000 0.050131216 0.0012 0.45 4001 0.050136856 Return 0.0112% Again, when the the input of F is increased by one unit, this will have following impact, ?2 F factor in on Q ?*L^?1 0.2 35000 8.106130831 0.2 35001 8.106177151 Return 0.0006% so by increasing F by 1 unit, will increase Q by 0.0006%. Finally the impact of K is as following, ?3 k factor in on Q ?*L^?1 0.3 4000 12.03976465 0.3 4001 12.04066755 Return 0.0075% it shows that if the value of K is increased by 1 unit it will increase the the Q by 0.0075%. Finally we can conclude that there exists a constant return to scale. this phenomenon is further justified by a fixed Exponent of the parameters in the function.

Related Questions

Navigate

• Browse (All)
• Browse 9
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.