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Created March 5, 2025 05:54
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Here’s an example using car manufacturing to illustrate how cheaper imported cars can affect a country’s standard of living, considering factors like productivity, labor market dynamics, and the potential role of tariffs.


Scenario Setup

Imagine a small country with a workforce of 200,000 people, divided between two sectors:

  • Car Manufacturing (Tradable Sector): Workers produce cars that can be sold domestically or imported from abroad.
  • Service Sector (Non-Tradable Sector): Workers provide services (e.g., retail, education) consumed only within the country.

Key Assumptions

  • Productivity:
    • Each worker in car manufacturing produces 2 cars per year.
    • In the service sector, productivity decreases as more workers join due to diminishing returns.
  • Prices:
    • In autarky (no trade), a car costs $25,000.
    • Under free trade, the world price of a car is $15,000.
  • Consumer Preferences: People value both cars and services, with a utility function ( U = C_T^{0.2} \cdot C_S^{0.8} ), where ( C_T ) is the number of cars consumed and ( C_S ) is the value of services in dollars.
  • Labor Allocation:
    • In autarky, 50,000 workers are in car manufacturing, and 150,000 are in services.

Life in Autarky (No Trade)

Production:

  • Car Manufacturing: 50,000 workers produce ( 50,000 \times 2 = 100,000 ) cars.
  • Service Sector: 150,000 workers produce services. Suppose the service output follows ( Q_S = 5,000,000 \cdot L_S^{0.6} ) (where ( L_S ) is the number of service workers), reflecting diminishing returns. Then:
    • ( Q_S = 5,000,000 \cdot 150,000^{0.6} ).
    • Compute ( 150,000^{0.6} \approx 1,500 ), so ( Q_S = 5,000,000 \cdot 1,500 = 7,500,000,000 ), or $7.5 billion.

Consumption:

  • The country consumes all it produces: 100,000 cars and $7.5 billion in services.

Welfare:

  • Utility is ( U_{\text{autarky}} = (100,000)^{0.2} \cdot (7,500,000,000)^{0.8} ).

Economic Snapshot:

  • Total income (GDP) is the value of cars plus services. If cars are valued at $25,000 each, car sector output is ( 100,000 \times 25,000 = 2.5 ) billion, so GDP = $2.5 billion + $7.5 billion = $10 billion.
  • Everyone is employed, and the economy balances high-productivity car jobs with service output.

Free Trade: Cheaper Imported Cars Flood In

Now, the country opens to free trade, and imported cars cost $15,000 each—much cheaper than the domestic cost of $25,000 (based on wages and productivity). The domestic car industry can’t compete and shuts down.

Production:

  • Car Manufacturing: 0 workers, 0 cars produced domestically.
  • Service Sector: All 200,000 workers shift to services. Using the same production function:
    • ( Q_S = 5,000,000 \cdot 200,000^{0.6} ).
    • Compute ( 200,000^{0.6} \approx 1,516 ), so ( Q_S = 5,000,000 \cdot 1,516 \approx 7,580,000,000 ), or $7.58 billion.

Income:

  • Total income is now $7.58 billion, all from services. This is less than the $10 billion in autarky because the high-productivity car jobs are lost, and adding more workers to services reduces average productivity due to diminishing returns.

Consumption:

  • Consumers spend 20% of income on cars and 80% on services (based on the utility function):
    • Cars: ( 0.2 \times 7.58 = 1.516 ) billion → ( C_T = \frac{1.516 \times 10^9}{15,000} \approx 101,067 ) cars.
    • Services: ( 0.8 \times 7.58 = 6.064 ) billion → ( C_S = 6.064 ) billion.

Welfare:

  • Utility is ( U_{\text{free}} = (101,067)^{0.2} \cdot (6,064,000,000)^{0.8} ).

Comparing to Autarky:

  • Autarky: ( C_T = 100,000 ), ( C_S = 7.5 ) billion.
  • Free Trade: ( C_T = 101,067 ), ( C_S = 6.064 ) billion.
  • Utility ratio: ( \frac{U_{\text{free}}}{U_{\text{autarky}}} = (1.0107)^{0.2} \cdot (0.8085)^{0.8} \approx 1.002 \cdot 0.846 \approx 0.848 < 1 ).
  • Result: Welfare falls under free trade. Although consumers buy slightly more cars, the drop in service consumption (due to lower income from lost productivity) outweighs this gain.

Why the Decline?

  • The shift from high-productivity car manufacturing (e.g., $50,000 value per worker in autarky) to a crowded service sector lowers overall income. Cheaper cars help, but not enough to offset the economic hit.

Adding a Tariff to Protect the Car Industry

Suppose the country imposes a $5,000 tariff on imported cars, raising their price to $20,000. This makes domestic production viable again to some extent.

Production:

  • Car Manufacturing: Assume 30,000 workers stay in the sector, producing ( 30,000 \times 2 = 60,000 ) cars, sold at $20,000 each. Value added might be $60,000 per worker (similar to autarky assumptions), totaling $1.8 billion.
  • Service Sector: 170,000 workers produce ( Q_S = 5,000,000 \cdot 170,000^{0.6} \approx 5,000,000 \cdot 1,700 = 8,500,000,000 ), or $8.5 billion.

Income:

  • Total income from production = $1.8 billion (cars) + $8.5 billion (services) = $10.3 billion.
  • Tariff Revenue: If consumers buy 100,000 cars total, imports = 100,000 - 60,000 = 40,000 cars. Revenue = ( 40,000 \times 5,000 = 200 ) million.
  • Effective Income: $10.3 billion + $0.2 billion = $10.5 billion.

Consumption:

  • Cars: ( 0.2 \times 10.5 = 2.1 ) billion → ( C_T = \frac{2.1 \times 10^9}{20,000} = 105,000 ) cars.
  • Services: ( 0.8 \times 10.5 = 8.4 ) billion.

Welfare:

  • Utility is ( U_{\text{tariff}} = (105,000)^{0.2} \cdot (8,400,000,000)^{0.8} ).
  • Compared to free trade (( C_T = 101,067 ), ( C_S = 6.064 ) billion), both ( C_T ) and ( C_S ) are higher, so ( U_{\text{tariff}} > U_{\text{free}} ).
  • Compared to autarky (( C_T = 100,000 ), ( C_S = 7.5 ) billion), ( C_T ) is higher, but ( C_S ) is slightly lower; welfare may still be below autarky but above free trade.

Impact:

  • The tariff keeps some workers in higher-productivity car jobs, reduces the strain on the service sector, and adds government revenue, improving welfare over unrestricted free trade.

Conclusion

In this car manufacturing example:

  • Free Trade: Cheaper imported cars ($15,000 vs. $25,000) benefit consumers but collapse the domestic industry, pushing workers into a less productive service sector. The resulting income drop lowers the standard of living compared to autarky.
  • With a Tariff: A $5,000 tariff raises the price to $20,000, sustaining some domestic production, maintaining higher productivity, and boosting welfare above the free trade scenario.

This shows how cheaper imports can harm a country’s standard of living if they disrupt high-productivity industries, and how a tariff can balance consumer savings with economic stability.

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