Question

GMCO produces three types of cars: compact, medium, and large. The variable cost per car and production capacity (per year) for each type of car are given as: The annual demand for each type of car depends on the prices of the

D=2500-100P+3Pₘ
three types of cars: Dₘ=1800+2P-30Pₘ+PL where, D,Dₘ, and DL espectively denote the demand
or compact, medium, and large cars, and P,Pₘ, and PL
​respectively denote the price for compact, medium, and large cars (prices are in thousands of dollars). Suppose that each compact car gets 30mpg, each medium car gets 25mpg, and each large car gets 18mpg. GMCO wants to keep the planet pollution free, so in addition to maximizing profit, it wants to maximize the average miles per gallon attained by the cars it sells. Construct a trade-off curve between these two objectives.
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Answer 1

Constructing a trade-off curve between GMCO's profit maximization and environmental sustainability involves analyzing the relationship between different car types, their pricing, demand, and fuel efficiencies. The optimal mix should align with maximizing profit and average mpg by adjusting car proportions, considering economies of scale and competitive pricing.

Step-by-step explanation:

To construct a trade-off curve between maximizing profit and maximizing the average miles per gallon (mpg) of cars sold by GMCO, we must consider that increasing the mix of cars with higher mpg (compacts and mediums) may decrease per-car profit margin but will increase overall fuel efficiency. Conversely, increasing the mix of less efficient but possibly more profitable large cars would lower the fleet average mpg. The trade-off curve will display the relationship between average mpg and profit, revealing how the company's average mpg changes as it adjusts the proportions of compact, medium, and large cars it sells in response to changes in market pricing and demand.

The demand equations given, namely D = 2500 - 100P + 3Pₘ for compact cars, Dₘ = 1800 + 2P - 30Pₘ + PL for medium cars, and another for large cars (not fully provided), represent how the price of each car type affects their respective demand levels. Maximizing profit involves setting production levels where MR (marginal revenue) = MC (marginal cost), considering the price elasticity of demand. To capture the environmental objective of maximizing average mpg, GMCO should aim for a product mix skewed towards more efficient cars, assuming the market allows for competitive pricing of these models.

The understanding of economies of scale, as illustrated by the concept where a single producer might hold a cost advantage with an output of 5,000 planes due to intersecting the LRAC curve at price P₁, could similarly apply to GMCO's car production. If it produces at a scale that aligns with the lowest point on the LRAC for car manufacturing, it can maximize profit while staying competitive. However, the additional objective of maximizing average mpg introduces complexity, requiring a balance between scale economies and environmental goals.