Question

RoboEats" is a startup that uses robots to deliver food to businesses and households. It operates a production function Q=10R0.5F0.5, where R are robots and F is food (no human labor involved!). The marginal products are MPR=5R-0.5F0.5 and MPF=5R0.5F-0.5. The price of renting a robot is pR=24, and the cost of an average meal is pF=9. The firm aims at making deliveries Q*=5000 meals per week.a) What is the optimal ratio of robots-to-food that minimizes the firm's cost? R/F= b) What is the optimal bundle of robots and food for the firm to use if target production is Q*=5000? R= F= c) Using this optimal bundle of inputs, what will be the firm's total cost? Cost= d) Now suppose we live in the times of COVID-19, and the demand for food deliveries skyrockets. However, in the short run, then number of robots is fixed at the optimal level found in part b). The firm wants to nevertheless increase production to Q*=6000 by scheduling multiple deliveries in a single route or offering discounts for larger orders. How many units of F should it input and what will be the total short-run cost? Short-run F= Short-run Cost= e) Now suppose we move to the long run ("the new normal") and the firm wants to keep its level of production at Q*=6000. What are the optimal quantities of Robots and Food that the firm should hire, and what is the total Cost? New long-run F= New long-run R= New long-run Cost= f) Now suppose that in "the new normal", the input price of food increases to pF=14. What is the new level of total Cost when the production is kept at Q*=6000? Cost= g) Does the production function feature increasing, constant, or decreasing returns to scale? Increasing Constant Decreasing

Answer 1

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