EC 330 Fall 2019 Your Name University Of Or

Ec 330 Fall 2019 Your Name University Of Or

Identify the core assignment questions by removing instructions, rubrics, and repetitive or meta-text content: the core task involves analyzing the market area for a factory based on transportation costs, with subsequent parts evaluating impacts of infrastructure investments, and questions about location strategies for breweries and wineries, clustering effects among entrepreneurs, and demographic calculations for city populations.

Paper For Above instruction

The region surrounding the city of Terminus presents a complex scenario for understanding market areas, transportation costs, and strategic location choices for manufacturing and service firms. This analysis begins with a detailed examination of the costs associated with widget production and distribution, then evaluates how infrastructure investments and technological upgrades influence market reach. Additionally, the paper explores spatial strategies of breweries and wineries in terms of proximity to inputs and markets, examines clustering effects among entrepreneurs, and concludes with demographic estimations of city populations within a region.

Analysis of Market Area Based on Transportation Costs

The initial step involves graphing the costs of producing widgets across a 150-mile region surrounding Terminus, which is situated at the western end. Given the data that the factory produces widgets at a cost of $10 per unit and transportation costs differ west and east of Terminus—$0.40 per mile west of Terminus and $0.10 per mile east—this creates a cost structure that shifts at the point of Terminus. The cost at the factory in Terminus is directly $10, serving as a benchmark. To the east, transport costs increase linearly at $0.10 per mile, rising from $10 at Terminus to $10 + ($0.10 × 100) = $20 at 100 miles east. To the west, transport costs increase at a steeper rate of $0.40 per mile, reaching $10 + ($0.40 × 50) = $30 at 50 miles west of Terminus.

Using this data, the costs along the region can be graphed with the cost curve starting at $10 at Terminus, decreasing to $10 at the factory location, increasing eastward by $0.10 per mile, and decreasing westward by $0.40 per mile—although the directionality creates a V-shaped cost structure. The key is to determine where the total costs of producing and transporting widgets are minimized compared to alternative production costs at home, which initially are $18.

Market Area with Original Costs ($10 factory cost)

Given the transport costs, the factory’s market area extends where the total delivered cost of widgets to customers is less than or equal to $18—the cost of making widgets at home. To the east, the transport cost per mile is $0.10, so the maximum distance east of Terminus where the factory can serve customers at a lower total cost is calculated as follows:

• Total cost at factory: $10
• Maximum transport cost allowed: $18 - $10 = $8
• Maximum east distance = $8 / $0.10 = 80 miles

Thus, the factory’s market zone extends 80 miles east of Terminus. To the west, the transport cost per mile is $0.40, so the maximum westward distance is:

• Maximum transport cost: $8
• Maximum west distance = $8 / $0.40 = 20 miles

Therefore, the market area is 20 miles west and 80 miles east of Terminus.

Adjusted Home Production Costs and Market Area

Next, the problem considers a revised scenario where the cost of making widgets at home is $16 east of Terminus and $20 west of Terminus, reflecting easier access and resource acquisition to the east. Recalculating the market area involves similar steps, but the comparison point shifts:

• To the east:
• Total maximum cost: $16
• Factory cost: $10
• Remaining for transport: $16 - $10 = $6
• Maximum east distance = $6 / $0.10 = 60 miles
• To the west:
• Total maximum cost: $20
• Factory cost: $10
• Remaining for transport: $20 - $10 = $10
• Maximum west distance = $10 / $0.40 = 25 miles

Thus, the adjusted market area now extends 25 miles west and 60 miles east of Terminus.

Impact of Infrastructure Investment and Technology Upgrade

The owners are considering two investments to expand their market: upgrading mountain roads to reduce westward transport costs to $0.20 per mile, or purchasing equipment to lower factory production costs to $8 per widget. Both options cost the same amount. To analyze their effects, assume a uniform distribution of consumers and calculate the change in market area resulting from each investment.

Impact of Road Upgrades

Reducing transport costs west of Terminus to $0.20 per mile alters the maximum westward distance as follows:

• Remaining cost allowance: $10 (factory cost) or the adjusted total maximum if considering the new cost structure.
• Maximum west distance (with improved roads): $10 / $0.20 = 50 miles.

Previously, at $0.40/mile, the maximum was 20 miles. Therefore, the upgrade adds:

• Additional miles = 50 - 20 = 30 miles.

Impact of Factory Cost Reduction

Lowering factory cost to $8 shifts the entire cost threshold downward, increasing the market radius on both sides:

• Maximum east distance: ($18 - $8) / $0.10 = $10 / $0.10 = 100 miles
• Maximum west distance: ($20 - $8) / $0.40 = $12 / 0.40 = 30 miles

Compared to initial bounds (80 miles east, 20 miles west), the new maximums imply an increase of:

• Eastward: 100 - 80 = 20 miles
• Westward: 30 - 20 = 10 miles

Thus, the factory’s market area would expand by 20 miles east and 10 miles west under the equipment upgrade.

Choosing Between Investments

The factory owners will compare the gains in market area—30 miles west versus 50 miles west for road improvement, and 20 miles east versus 80 miles east for factory cost reduction. Given the similar costs of the investments, the decision hinges on which expansion provides the larger market coverage. The data indicates upgrading roads adds 30 miles west, while installing new equipment adds only 10 miles west but 20 miles east. Overall, the decision will depend on which market extension aligns better with consumer demand and profitability considerations, but purely from a geographic scope perspective, the infrastructure upgrade offers broader westward reach, and the equipment upgrade offers broader eastward reach.

Strategies of Breweries and Wineries: Location Analysis

Most breweries tend to be located close to their customers and away from primary input sources because of market orientation. Consumers are often found in urban or densely populated regions, making proximity to these markets essential for reducing transportation costs and ensuring product freshness. In contrast, wineries typically locate closer to their primary input sources, such as vineyards, which require specific climatic and soil conditions. Since wine production is often less dependent on rapid distribution to urban markets, proximity to vineyards minimizes input costs and supports high-quality production.

Clustering Effects among Entrepreneurs

Clustering among entrepreneurs increases labor costs because more local competition can inflate wages and operational expenses. However, it facilitates economies of scale in materials and knowledge spillovers, reducing per-unit costs. These effects make clustering advantageous as it balances higher labor costs with savings in materials procurement and innovation sharing, thus optimizing overall profitability. The total cost per piece decreases with the number of entrepreneurs up to a point where diminishing returns and increased competition may offset benefits, suggesting an equilibrium cluster size that maximizes profits.

Demographic Estimations of City Populations

The second-largest city in a region with 8 million inhabitants implies the total population of the region is at least a multiple where the second city’s population is known. If data suggests that the second-largest city contains, for example, 2 million residents, and the pattern of city sizes follows a common demographic distribution (e.g., Zipf's law), the largest city might be estimated at a slightly higher population. Conversely, for calculations of the fourth and tenth-largest cities, the population sizes depend on the specific ranking ratios, which are often modeled by demographic rank-size rules, implying the largest city could have around 3 million, the fourth approximately 1 million, and the tenth about 300,000 residents, depending on the specific regional distribution.

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