Perfectly competitive firm Doggies Paradise Inc. sells...

Perfectly competitive firm Doggies Paradise Inc. sells winter coats for dogs. Dog coats sell for $\$ 72$ each. The fixed costs of production are $\$ 100 .$ The total variable costs are $\$ 64$ for one unit, $\$ 84$ for two units, $\$ 114$ for three units, $\$ 184$ for four units, and $\$ 270$ 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). On one diagram, sketch the total revenue and total cost curves. On another diagram, sketch the marginal revenue and marginal cost curves. What is the profit maximizing quantity?

Perfectly competitive firm Doggies Paradise Inc. sells winter coats for dogs. Dog coats sell for $\$ 72$ each. The fixed costs of production are $\$ 100 .$ The total variable costs are $\$ 64$ for one unit, $\$ 84$ for two units, $\$ 114$ for three units, $\$ 184$ for four units, and $\$ 270$ 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). On one diagram, sketch the total revenue and total cost curves. On another diagram, sketch the marginal revenue and marginal cost curves. What is the profit maximizing quantity?

Key Concepts

Perfect Competition

In a perfectly competitive market, individual firms are price takers with no control over the market price. This concept implies that each firm must accept the prevailing market price, and its decision on output is guided solely by its cost structure and prevailing prices. The firm’s objective is to maximize profits by producing at a level where marginal cost equals marginal revenue.

Fixed and Variable Costs

Understanding fixed and variable costs is fundamental in cost analysis. Fixed costs remain constant regardless of the output level, while variable costs change with the quantity produced. These two cost components together determine the total cost of production and are essential for analyzing profitability and economies of scale.

Total Revenue and Total Cost Analysis

Total revenue is calculated by multiplying the price of the product by the quantity sold, whereas total cost is the sum of fixed and variable costs incurred in production. Analyzing these values helps firms assess profitability across different output levels and understand the overall cost structure, which is crucial for decision-making in production and pricing strategies.

Marginal Revenue and Marginal Cost Analysis

Marginal revenue is the additional revenue generated from selling one more unit, and marginal cost is the additional cost incurred from producing one additional unit. In a perfectly competitive market, the marginal revenue equals the market price. Analyzing these marginal values is critical as they help determine the optimal level of production where profit is maximized.

Profit Maximization

Profit maximization occurs at the output level where marginal revenue equals marginal cost. At this point, producing any additional unit would cause the cost to exceed the revenue, and producing fewer units would leave potential profit unexploited. This concept underpins the decision-making process in production economics, guiding firms to adjust output to achieve the highest possible profits.

Transcript

00:01 In this problem, we know that we are producing between one and five output levels.

00:05 So the first thing that we are going to fill out is the fixed cost.

00:09 We know that the fixed cost is going to be the same for all levels of production.

00:13 So it's always going to be $100.

00:18 So it's going to be $100 for all levels of output.

00:22 And it says that the total variable cost for one unit is 64.

00:27 The total variable cost for two units is 84.

00:30 Total variable cost for three units is 114.

00:35 Total variable cost for four units is 184.

00:38 The total variable cost for five units is 270.

00:44 And now the total revenue is simply equal to, total revenue is equal to price times quantity.

00:53 And when our price is equal to 72, as it is always equal to, our total revenue is going to be equal to 72.

01:02 Then 144, then 216, then 288, then 360.

01:12 Now we have to go to our marginal revenue.

01:16 Our marginal revenue is simply what is the difference between, or what is the amount of revenue added by one additional unit sold, of goods sold.

01:26 So we don't have anything for our first marginal revenue.

01:30 Going from one to two units, we get 72.

01:33 From 2 to 3, we get 72.

01:35 3 to 4 we get 72, and 4 to 5 we get 72.

01:40 Now, our total cost is equal to fixed cost plus variable cost.

01:45 So we just have to take the sum of these two columns.

01:48 So this is equal to 164, is equal to 184, is equal to 214, this is equal to 214, and this is equal to 370.

02:00 And now we have to come up with the marginal cost.

02:02 The marginal cost is just the cost associated, or the change in cost, the change in total cost associated with hiring one more additional, or selling one more additional good, or producing one more additional good.

02:15 So we have nothing in our marginal cost, one, going from 164 to 184, there's a $20 cost increase, 184 to $2 .14, there's a $30 cost increase.

02:28 Going from 218 to 284, there's a $70 cost increase, and then going from 284 to $370, there's an $86 cost increase.

02:39 Now, to calculate profit, we are simply going to take total revenue minus total cost.

02:43 So, 72 minus 164 is negative 92, negative 92.

02:53 Then 144 minus 184 is equal to negative 40...

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