The AAA Aquarium Co. sells aquariums for \(\$ 20\) each. Fixed costs of production are \(\$ 20 .\) The total variable costs are \(\$ 20\) for one aquarium, \(\$ 25\) for two units, \(\$ 35\) for the three units, \(\$ 50\) for four units, and \(\$ 80\) for five units. In the form of a table, calculate total revenue, marginal revenue, total cost, and marginal cost for each output level (one to five units). What is the profit-maximizing quantity of output? On one diagram, sketch the total revenue and total cost curves. On another diagram, sketch the marginal revenue and marginal cost curves.

Short Answer

Expert verified
In conclusion, the profit-maximizing quantity of output for the AAA Aquarium Co. is 3 units, where the marginal revenue (\(\$20\)) equals the marginal cost (\(\$20\)). The total revenue, marginal revenue, total cost, and marginal cost calculations for each output level are as follows: - 1 Unit: Total Revenue = \(\$20\), Marginal Revenue = -, Total Cost = \(\$40\), Marginal Cost = -. - 2 Units: Total Revenue = \(\$40\), Marginal Revenue = \(\$20\), Total Cost = \(\$45\), Marginal Cost = \(\$5\). - 3 Units: Total Revenue = \(\$60\), Marginal Revenue = \(\$20\), Total Cost = \(\$55\), Marginal Cost = \(\$10\). - 4 Units: Total Revenue = \(\$80\), Marginal Revenue = \(\$20\), Total Cost = \(\$70\), Marginal Cost = \(\$15\). - 5 Units: Total Revenue = \(\$100\), Marginal Revenue = \(\$20\), Total Cost = \(\$100\), Marginal Cost = \(\$30\). Sketching the total revenue, total cost, marginal revenue, and marginal cost curves can aid in visualizing their relationships.

Step by step solution

01

Calculate Total Revenue

To calculate total revenue for each output level, we will multiply the number of units sold by the price per unit \(\(\$20)\). - 1 Unit: \(\$20\times1=\$20) - 2 Units: \(\$20\times2=\$40) - 3 Units: \(\$20\times3=\$60) - 4 Units: \(\$20\times4=\$80) - 5 Units: \(\$20\times5=\$100)
02

Calculate Marginal Revenue

To calculate marginal revenue, we will find the difference in total revenue between each consecutive output level. - 1 Unit: - (No preceding output level) - 2 Units: \(\$40-\$20=\$20) - 3 Units: \(\$60-\$40=\$20) - 4 Units: \(\$80-\$60=\$20) - 5 Units: \(\$100-\$80=\$20)
03

Calculate Total Cost

We are already given the total cost for each output level. Here they are for reference: - 1 Unit: \(\$20+\$20=\$40) - 2 Units: \(\$20+\$25=\$45) - 3 Units: \(\$20+\$35=\$55) - 4 Units: \(\$20+\$50=\$70) - 5 Units: \(\$20+\$80=\$100)
04

Calculate Marginal Cost

To calculate marginal cost, we will find the difference in total cost between each consecutive output level. - 1 Unit: - (No preceding output level) - 2 Units: \(\$45-\$40=\$5) - 3 Units: \(\$55-\$45=\$10) - 4 Units: \(\$70-\$55=\$15) - 5 Units: \(\$100-\$70=\$30)
05

Determine Profit-Maximizing Quantity of Output

To find the profit-maximizing quantity of output, we will look for the output level at which marginal revenue equals marginal cost. In this case, the output level is at 3 units, where both marginal revenue and marginal cost are \(\$20\).
06

Sketch the Total Revenue and Total Cost Curves

To sketch the total revenue and total cost curves, we will plot the total revenue and total cost for each output level on a graph. Since it's just a sketch, it does not need to be perfectly accurate. Just draw a line that increases linearly for the total revenue curve and a curved line for the total cost curve.
07

Sketch the Marginal Revenue and Marginal Cost Curves

To sketch the marginal revenue and marginal cost curves, plot the marginal revenue and marginal cost values for each output level on a separate graph. Draw a horizontal line for the marginal revenue curve, since it remains constant at \(\$20\). Draw a curvy line going through the marginal cost points, showing that it increases as the output level increases. In conclusion, the profit-maximizing quantity of output for the AAA Aquarium Co. is 3 units, where the marginal revenue equals the marginal cost. Sketching the curves can assist in visualizing the relationships between total revenue, total cost, marginal revenue, and marginal cost.

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