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Production of taxi rides - GlobalTaxi runs taxi services around the globe. GlobalTaxi uses two inputs in production

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3. Production of taxi rides (15%)

GlobalTaxi runs taxi services around the globe. GlobalTaxi uses two inputs in production: capital K and labor L. Capital has a rental cost of r, while labor is paid a wage w.

(a) Derive the expression for GlobalTaxi’s isocost function with labor on the right-hand side, and explain what it means.

(b) Explain what happens to the slope of the isocost function when the wage w increases. How will an increase in w typically affect the choice of inputs for a company that has a smoothly declining marginal rate of technical substitution? Why?

(c) Let’s fast forward to the year 2030, where GlobalTaxi is now producing taxi rides with the following production function for offering a certain number of taxi rides T : T = H + D, where H is a taxi ride delivered by a Human driver, and D is a taxi ride delivered by a Driverless car (or robot driver). Hold the number of taxi rides T constant. 2 • Derive an expression for the number of driverless taxi rides D needed to reach the number T of taxi rides, given a certain number H of human taxi rides. • What do we call the expression you derived? • Draw a diagram with D on the vertical axis and H on the horizontal axis. Plot the derived function for values T = 50, T = 100, T = 150.

(d) Still in the year 2030, to organize a taxi ride by a human driver, GlobalTaxi needs to pay a cost w′, which includes the wage of the taxi driver and the rental cost of a regular car. In contrast, the cost to organize a ride by a driverless car is given by r. GlobalTaxi has a branch in Norway, where the factor cost ratio (w′/r) is 2, while in the USA, this factor cost ratio is (1/2). Suppose GlobalTaxi supplies 100 taxi rides in each of these two countries and minimizes the cost to do so. How many human and how many driverless taxi rides does GlobalTaxi use (i) in Norway and (ii) in the USA? Illustrate your answer on a separate diagram for each country, depicting that country’s isoquants and isocosts. Explain your answer.

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