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?

Step by step solution

01

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)

02

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.

03

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)

04

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).

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