Assume that the demand curve D(p) given below is the market demand for widgets:

Q=D(p)=1723−14p𝑄=𝐷(𝑝)=1723-14𝑝, p > 0

Let the market supply of widgets be given by:

Q=S(p)=−5+10p𝑄=𝑆(𝑝)=-5+10𝑝, p > 0

where p is the price and Q is the quantity. The functions D(p) and S(p) give the number of widgets demanded and supplied at a given price.

To find the equilibrium price and quantity in this market, we need to set the demand and supply equal to each other because equilibrium occurs where the quantity demanded equals the quantity supplied.

We are given the following demand and supply functions:

\[
Q = D(p) = 1723 - 14p
\]
\[
Q = S(p) = -5 + 10p
\]

### Step 1: Set \(D(p)\) equal to \(S(p)\)
\[
1723 - 14p = -5 + 10p
\]

### Step 2: Solve for \(p\) (equilibrium price)

First, add \(14p\) to both sides to eliminate the \(-14p\) on the left-hand side:

\[
1723 = -5 + 24p
\]

Next, add 5 to both sides to eliminate \(-5\) on the right-hand side:

\[
1728 = 24p
\]

Now, solve for \(p\) by dividing both sides by 24:

\[
p = \frac{1728}{24} = 72
\]

Thus, the equilibrium price is \(p = 72\).

### Step 3: Solve for \(Q\) (equilibrium quantity)

To find the equilibrium quantity, substitute \(p = 72\) into either the demand or supply function. Using the demand function:

\[
Q = D(72) = 1723 - 14(72)
\]
\[
Q = 1723 - 1008 = 715
\]

Thus, the equilibrium quantity is \(Q = 715\).

### Conclusion:
- **Equilibrium price**: \(p = 72\)
- **Equilibrium quantity**: \(Q = 715\)

Let me know if you'd like further details or have any questions!

Here are 5 related questions for exploration:
1. How does a shift in the demand curve affect the equilibrium price and quantity?
2. What happens if the supply curve shifts due to a change in production costs?
3. Can equilibrium be reached if the price is fixed below the equilibrium price?
4. What is the effect of government-imposed price ceilings on this market?
5. How can elasticity of demand and supply influence market adjustments?

**Tip**: To analyze the impact of shifts in demand or supply, compare new equilibrium points by adjusting the corresponding function.

Assume that the demand curve D(p) given below is the market demand for widgets: Q = D(p) = 1723 - 14p, p > 0. Let the market supply of widgets be given by: Q = S(p) = -5 + 10p, p > 0, where p is the price and Q is the quantity. The functions D(p) and S(p) give the number of widgets demanded and supplied at a given price.

This detailed guide shows how to solve for the equilibrium price and quantity using the demand and supply functions: D(p) = 1723 - 14p and S(p) = -5 + 10p. The solution involves algebraic manipulation to find equilibrium in the market for widgets, suitable for advanced high school or undergraduate economics students.

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