A Model of Manufacturers and Buyers of Cars Over the Business Cycle Illustrating Competitive Manufacturing: Advanced Study

I illustrate competitive manufacturing with a simple numerical model of manufacturers and buyers of
cars over a business cycle with off-peak and peak demand periods. My model has two types of plants
manufacturing cars, plantK and plantL, each having linear total costs with absolute capacity limits.
PlantK operates with low VC and high FC. PlantK, because of its low VC, produces continuously
at capacity in off-peak and in peak periods. PlantL, because of its high VC, shut-downs in off-peak
periods and produces at capacity in peak periods. I show results under perfect competition SRMC
pricing. I prove mathematically two propositions with this model. Proposition I shows mathematically
the conditions of investor indifference to choose between PlantsK and PlantsL. The significance is
to show a positive aspect of PlantsL, its output-rate flexibility, that some may overlook. Proposition
II shows mathematically the conditions that shifting consumption of car purchases from off-peak to
peak necessarily adds to consumer surplus. The significance is to show the importance of increasing
consumer purchases in peak periods. These two propositions are intuitive and common sense.