Question

In a closed economy, there are four firms. The following diagram shows their sales. $$ \begin{array}{lccc} \text { Firm } & \text { Sells } & \text { To } & \text { For } \\ \text { Iron Mine Inc. } & \text { Iron One } & \text { United Steel Co. } & \$ 100 \\ \text { United Steel Co. } & \text { Steel } & \text { Acme Automobiles } & \$ 300 \\ \text { Acme Automobiles } & \text { Cars } & \text { Honest John's Car } & \\\ & & \text { Dealership } & \$ 500 \end{array} $$ Honest John's Car Dealership Cars Consumers $$\$ 1000$$ 1.) Calculate value added by each firm. 2.) Calculate GNP using both the value-added approach and the final goods approach. 3.) A value-added tax of \(10 \%\) is imposed. Calculate each firm's tax payment and tax receipts for the economy. 4.) Compare the results of a \(10 \%\) value-added tax with a \(10 \%\) sales tax imposed on final goods, is there a difference in total tax collected?

Short answer

The value added by each firm is: Iron Mine Inc. - \(\$100), United Steel Co. - \(\$200), Acme Automobiles - \(\$200), and Honest John's Car Dealership - \(\$500). The GNP calculated using the value-added and final goods approach is the same, both being \(\$1000). Under a 10% value-added tax, the total tax receipts for the economy are \(\$100), which is the same as under a 10% sales tax imposed on final goods. Therefore, there is no difference in total tax collected in both tax scenarios.

Step-by-step solution

Calculate the value added by each firm

Value-added for each firm is calculated as the difference between the value of its output (sales) and its input (purchases). In this case: 1. Iron Mine Inc.: Value added = \(\$100 - $0) = \(\$100) as there is no input cost. 2. United Steel Co.: Value added = \(\$300 - $100) = \(\$200) 3. Acme Automobiles: Value added = \(\$500 - $300) = \(\$200) 4. Honest John's Car Dealership: Value added = \(\$1000 - $500) = \(\$500)

Calculate GNP using value-added and final goods approaches

2.1. Value-Added Approach: We sum up the value added by each firm: GNP = \(\$100 + \(200 + \)200 + $500) = \(\$1000) 2.2. Final Goods Approach: Since only the car dealership sells to the consumers, the GNP is equal to its sales: GNP = \(\$1000) We see that the GNP calculated using both methods is the same, which validates the calculations.

Calculate tax payments and tax receipts under a 10% value-added tax

A 10% value-added tax implies that each firm pays a tax on the value it adds to the product. Using the value added by each firm, we get tax payments as follows: 1. Iron Mine Inc.: Tax payment = \(10\% \times $100) = \$10 2. United Steel Co.: Tax payment = \(10\% \times $200) = \$20 3. Acme Automobiles: Tax payment = \(10\% \times $200) = \$20 4. Honest John's Car Dealership: Tax payment = \(10\% \times $500) = \$50 Total tax receipts for the economy = \(\$10 + \(20 + \)20 + $50) = \(\$100)

Compare the results of a 10% value-added tax with a 10% sales tax imposed on final goods

If a 10% sales tax is imposed on final goods, it means that the tax is only applicable on the final sale of goods. In our case, this will only be applied to Honest John's Car Dealership, as they are selling directly to the consumers: Sales tax = \(10\% \times $1000) = \(\$100) When comparing the two tax scenarios, we conclude that there is no difference in total tax collected. In both cases, the total tax collected by the economy is \(\$100).

Key concepts

Value-Added Tax

A value-added tax (VAT) is a type of indirect tax that is imposed at each stage of the production and distribution process. Unlike a sales tax, which is only charged at the point of final sale, VAT is applied incrementally. Each firm involved in the supply chain adds value to the product, and VAT is charged on that added value.

For example, consider a supply chain starting with raw material extraction and ending with the sale to the final consumer. Each firm along this chain would calculate VAT based on the difference between their sales and their input costs, which is the value they add. This ensures that the tax is effectively spread over each stage of production.

This mechanism prevents double taxation as each firm receives credits for the tax already paid on inputs, contributing to a smoother flow of goods and a broad tax base. As seen in our problem, Iron Mine Inc., United Steel Co., Acme Automobiles, and Honest John's Car Dealership, all add value at different stages, and the VAT of 10% was charged accordingly on each firm's value addition.

Sales Tax

Sales tax operates differently from value-added tax in that it is typically imposed solely at the point of final sale to the consumer. This means that the entire tax burden is borne by the end consumer and is calculated as a percentage of the retail price of the goods.

In the example scenario, a sales tax of 10% was levied only when Honest John's Car Dealership sold cars to consumers. Unlike a VAT, which would have been collected at various stages throughout the supply chain, the sales tax is a singular application that simplifies administration but concentrates tax impact at the end transaction.

Sales tax can be less complex to implement because it requires collecting and assessing the tax only once in the retail sale. Nevertheless, it can lead to inefficiencies, such as higher prices for consumers who are left covering the entire tax, and it does not reflect the incremental contributions of value as in VAT.

Closed Economy

A closed economy is a self-sufficient economic system that does not engage in international trade. All economic activities, including consumption, production, and investment, are restricted to within the country's borders. This assumption allows analysts to study the internal mechanisms of economic growth without interference from external factors like imports or exports.

In the exercise scenario with the four firms, we observe a closed economy where all transactions take place domestically. This setup simplifies the calculation of metrics like GNP (Gross National Product) because there is no need to adjust for external trade balances. The absence of foreign transactions makes it easier to apply taxation methods like VAT and sales tax without the complexity of international tax compliance.

By focusing solely on domestic activities, a closed economy enables a firm understanding of internal market dynamics, which can be instructive for economic policy development focused purely on internal affairs.

Value-Added Approach

The value-added approach is a method of calculating economic inputs by summing up the value added at each production stage in the economy. This method identifies how much value each firm adds to a product as it moves through the supply chain, and is pivotal for understanding contributions to overall economic output from different sectors.

During our exercise, each firm, from Iron Mine Inc. to Honest John's Car Dealership, added a certain amount of value as they transformed raw materials into final products. The value added by each firm is calculated as the difference between the sales revenue they generate from selling their goods and the cost of their inputs.

• Iron Mine Inc. had no inputs, so its value addition was the entirety of its output, $100.
• United Steel Co. added $200 in value after buying iron for $100 and producing steel for $300.
• Acme Automobiles further added $200, shifting from $300 steel to $500 cars.
• Honest John's Car Dealership’s contribution was $500, the difference between what they bought ($500) and their sales ($1000).

Totaling these, the economy's GNP through the value-added approach equates to $1000, highlighting each firm's role in sustaining economic flow.