The Jesaki Research Department Established The Following Price-supply Function For Widgets:$ Q(x) = 2.01x + 41 $where $ X $ Is In Thousands Of Widgets. Find The Equilibrium Quantity. Use That Information To Complete The Following

The Equilibrium Quantity of Widgets: A Mathematical Analysis

In the world of economics, the concept of equilibrium quantity is crucial in understanding the behavior of supply and demand in a market. The equilibrium quantity is the point at which the quantity supplied equals the quantity demanded, resulting in a stable market price. In this article, we will explore the equilibrium quantity of widgets using the price-supply function established by the Jesaki research department.

The price-supply function for widgets is given by the equation:

$$q(x) = 2.01x + 41$$

where $x$ is the quantity supplied in thousands of widgets. This equation represents the relationship between the quantity supplied and the price of widgets.

To find the equilibrium quantity, we need to set the quantity supplied equal to the quantity demanded and solve for $x$. However, we are not given the demand function. Instead, we are given the price-supply function, which represents the relationship between the quantity supplied and the price.

Since we are not given the demand function, we cannot directly find the equilibrium quantity using the usual method of setting quantity supplied equal to quantity demanded. However, we can use the price-supply function to find the equilibrium price and then use that information to find the equilibrium quantity.

To find the equilibrium price, we need to find the price at which the quantity supplied equals the quantity demanded. However, as mentioned earlier, we are not given the demand function. Instead, we can use the price-supply function to find the price at which the quantity supplied is maximized.

To find the price at which the quantity supplied is maximized, we need to find the vertex of the price-supply function. The vertex of a linear function is given by the equation:

$$x = -\frac{b}{2a}$$

where $a$ and $b$ are the coefficients of the linear function. In this case, the price-supply function is:

$$q(x) = 2.01x + 41$$

The coefficient of $x$ is $2.01$, and the constant term is $41$. Therefore, the vertex of the price-supply function is given by:

$$x = -\frac{41}{2(2.01)}$$

Simplifying this expression, we get:

$$x = -\frac{41}{4.02}$$

$$x = -10.2$$

However, since $x$ represents the quantity supplied in thousands of widgets, it cannot be negative. Therefore, we need to find the price at which the quantity supplied is maximized using a different method.

To find the price at which the quantity supplied is maximized, we can use the fact that the quantity supplied is maximized when the price is equal to the slope of the price-supply function. The slope of the price-supply function is given by the coefficient of $x$, which is $2.01$. Therefore, the price at which the quantity supplied is maximized is:

$$p = 2.01(1000)$$

$$p = 2010$$

This is the price at which the quantity supplied is maximized.

Now that we have found the price at which the quantity supplied is maximized, we can use that information to find the equilibrium quantity. To do this, we need to substitute the price into the price-supply function and solve for $x$.

Substituting the price into the price-supply function, we get:

$$q(x) = 2.01x + 41$$

$$2010 = 2.01x + 41$$

Subtracting $41$ from both sides, we get:

$$1969 = 2.01x$$

Dividing both sides by $2.01$, we get:

$$x = \frac{1969}{2.01}$$

Simplifying this expression, we get:

$$x = 980.5$$

Therefore, the equilibrium quantity is approximately $980.5$ thousand widgets.

In this article, we used the price-supply function established by the Jesaki research department to find the equilibrium quantity of widgets. We first found the price at which the quantity supplied is maximized using the fact that the quantity supplied is maximized when the price is equal to the slope of the price-supply function. We then substituted this price into the price-supply function and solved for $x$ to find the equilibrium quantity. The equilibrium quantity is approximately $980.5$ thousand widgets.

The equilibrium quantity of widgets is an important concept in economics, as it represents the point at which the quantity supplied equals the quantity demanded, resulting in a stable market price. In this article, we used the price-supply function established by the Jesaki research department to find the equilibrium quantity. We first found the price at which the quantity supplied is maximized using the fact that the quantity supplied is maximized when the price is equal to the slope of the price-supply function. We then substituted this price into the price-supply function and solved for $x$ to find the equilibrium quantity.

The equilibrium quantity of widgets is affected by various factors, including changes in the price of widgets, changes in the cost of production, and changes in consumer demand. Therefore, it is essential to understand the factors that affect the equilibrium quantity of widgets in order to make informed decisions in the market.

• Jesaki Research Department. (n.d.). Price-Supply Function for Widgets.
• Samuelson, P. A., & Nordhaus, W. D. (2010). Economics. McGraw-Hill.

Note: The references provided are fictional and for demonstration purposes only.
Q&A: Equilibrium Quantity of Widgets

In our previous article, we explored the equilibrium quantity of widgets using the price-supply function established by the Jesaki research department. In this article, we will answer some frequently asked questions about the equilibrium quantity of widgets.

A: The equilibrium quantity of widgets is the point at which the quantity supplied equals the quantity demanded, resulting in a stable market price. In our previous article, we found that the equilibrium quantity of widgets is approximately 980.5 thousand widgets.

A: The equilibrium quantity of widgets is affected by changes in the price of widgets. If the price of widgets increases, the quantity supplied will also increase, resulting in a higher equilibrium quantity. Conversely, if the price of widgets decreases, the quantity supplied will decrease, resulting in a lower equilibrium quantity.

A: The equilibrium quantity of widgets is affected by changes in the cost of production. If the cost of production increases, the quantity supplied will decrease, resulting in a lower equilibrium quantity. Conversely, if the cost of production decreases, the quantity supplied will increase, resulting in a higher equilibrium quantity.

A: The equilibrium quantity of widgets is affected by changes in consumer demand. If consumer demand increases, the quantity supplied will also increase, resulting in a higher equilibrium quantity. Conversely, if consumer demand decreases, the quantity supplied will decrease, resulting in a lower equilibrium quantity.

A: The price-supply function is a mathematical representation of the relationship between the quantity supplied and the price of widgets. The equilibrium quantity of widgets is the point at which the quantity supplied equals the quantity demanded, resulting in a stable market price. In our previous article, we used the price-supply function to find the equilibrium quantity of widgets.

A: The equilibrium quantity of widgets can be used in real-world applications such as:

• Market analysis: The equilibrium quantity of widgets can be used to analyze the behavior of the market and make informed decisions.
• Production planning: The equilibrium quantity of widgets can be used to plan production and meet the demands of consumers.
• Pricing strategy: The equilibrium quantity of widgets can be used to determine the optimal price of widgets.

In this article, we answered some frequently asked questions about the equilibrium quantity of widgets. We discussed how the equilibrium quantity of widgets is affected by changes in the price of widgets, changes in the cost of production, and changes in consumer demand. We also discussed the relationship between the price-supply function and the equilibrium quantity of widgets. The equilibrium quantity of widgets is an important concept in economics, and it can be used in real-world applications such as market analysis, production planning, and pricing strategy.

• Jesaki Research Department. (n.d.). Price-Supply Function for Widgets.
• Samuelson, P. A., & Nordhaus, W. D. (2010). Economics. McGraw-Hill.

Note: The references provided are fictional and for demonstration purposes only.