1. Consider a bus company serving T number of passengers. To serve these passengers, the company needs to hire drivers and rent buses. Letting L denote the number of drivers and K the number of buses, the production function is given by T= (sq. rt.)LK.
The wage per driver is 2 and the rental cost per bus is 4. The company minimizes costs by choice of L and K subject to the constraint that this company must serve T passengers. The cost minimization problem is written minL,K 2L+ 4K, s.t. (sq. rt.)LK= T
(a) At the optimum, there is a specic relationship between L and K. Derive this relationship. (Hint: Derive the slopes of the iso-quant and the iso-cost curves and set them equal.)
(b) Substitute this relationship into the production constraint to obtain the optimal L and K as functions of T.
(c) Derive the cost function.
(d) Does the cost function yield increasing or decreasing returns to scale or constant returns to scale? Why is it so? Draw a curve illustrating the cost function.