Question

The market for smoothies is perfectly competitive. The table in the next column sets out the market demand schedule. $$\begin{array}{cc} \begin{array}{c} \text { Price } \\ \text { Idollars per smoothie] } \end{array} & \begin{array}{c} \text { Quantity demanded } \\ \text { (smoothies per hour) } \end{array} \\ \hline 1.90 & 1,000 \\ 2.00 & 950 \\ 2.20 & 800 \\ 2.91 & 700 \\ 4.25 & 550 \\ 5.25 & 400 \\ 5.50 & 300 \end{array}$$ Each of the 100 producers of smoothies has the following costs when it uses its least-cost plant: $$\begin{array}{cccc} & & \text { Average } & \text { Average } \\ \text { Output } & \text { Marginal cost } & \text { variable cost } & \text { fotal cost } \\ \begin{array}{c} \text { (smoothies } \\ \text { per hour) } \end{array} & \begin{array}{c} \text { (dollars per } \\ \text { additional smoothie) } \end{array} & \text { (dollars per smoothie) } \\ \hline 3 & 2.50 & 4.00 & 7.33 \\ 4 & 2.20 & 3.53 & 6.03 \\ 5 & 1.90 & 3.24 & 5.24 \\ 6 & 2.00 & 3.00 & 4.67 \\ 7 & 2.91 & 2.91 & 4.34 \\ 8 & 4.25 & 3.00 & 4.25 \\ 9 & 8.00 & 3.33 & 4.44 \end{array}$$ a. What is the market price of a smoothie? b. What is the market quantity of smoothies? c. How many smoothies does each firm sell? d. What is the economic profit made or economic loss incurred by each firm?

Short answer

The market price is $2.20, with a market quantity of 800 smoothies per hour. Each firm sells 8 smoothies, making no economic profit or loss.

Step-by-step solution

Determine the market equilibrium price

First, identify the price where the quantity demanded equals the quantity supplied. In a perfectly competitive market, the price is set where marginal cost (MC) equals the market price (P). Analyze the tables given and find the price that matches the marginal cost.

Find the equilibrium quantity

Once the equilibrium price (P) is identified, look at the corresponding quantity demanded in the market demand schedule table. This gives the total quantity of smoothies demanded at the equilibrium price.

Find the quantity each firm supplies

Use the equilibrium price to find out the output level for each firm where MC equals the equilibrium price. The firm’s output at this equilibrium price level is the quantity each firm supplies.

Calculate individual firm's revenue

Determine each firm's revenue by multiplying the equilibrium price by the quantity of smoothies each firm sells.

Calculate economic profit or loss

Finally, find the economic profit or loss incurred by each firm by comparing total revenue with total cost (use the total cost corresponding to the output level each firm supplies).

Key concepts

Market Equilibrium

In a perfectly competitive market like the market for smoothies, the price of goods is determined by the interaction of supply and demand. Market equilibrium occurs when the quantity of smoothies that consumers want to buy equals the quantity that producers want to sell. To find this point, we need to compare the market demand schedule (which shows how many smoothies consumers will buy at different prices) with the producers’ marginal cost (which shows the cost of producing an additional smoothie). At equilibrium, the price at which quantity demanded equals quantity supplied becomes the market price. For smoothies, this means analyzing the tables provided and identifying the price where the quantity demanded matches the quantity supplied by the aggregate supply of all producers.

Marginal Cost

Marginal cost (MC) is crucial in determining the supply side of the market. It is the additional cost of producing one more unit of output. In a perfectly competitive market, firms set their supply based on marginal cost. For instance, if producing one more smoothie costs a firm \(2, they will continue to produce until the market price drops to \)2. If the market price is higher, say \(3, firms will produce more until the price equals the marginal cost. Using the provided producer cost table, we can see how marginal cost changes with output levels, making it easier to determine the point where MC equals the market price. For example, if the market price is \)2.20, firms will produce at the output level where marginal cost is approximately $2.20, ensuring they neither overproduce nor underproduce.

Economic Profit

Economic profit is the difference between a firm's total revenue and total costs (including both explicit and implicit costs). In the smoothie market, each firm's economic profit can be found by first calculating their total revenue, which is done by multiplying the equilibrium price by the number of smoothies each firm sells. Next, we compare this revenue to their total costs at the given output level. Using the firm's cost data, we can see if firms are making a profit or a loss. If we find that total revenue exceeds total cost, the firm makes an economic profit. Conversely, if total cost is higher than total revenue, the firm incurs an economic loss. This concept helps us understand whether firms will remain in the market or exit in the long run based on their profitability.