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To determine the market supply equation, we need to sum the individual supply equations provided.

The given equations are:

\[ P_1 = 10 + Q_1 \]
\[ P_2 = 18 + 0.5Q_2 \]
\[ P_3 = 16 + 0.4Q_3 \]

Since we are interested in the market supply, we need to express the quantities \( Q_1 \), \( Q_2 \), and \( Q_3 \) in terms of price (\( P \)) and then sum them up.

First, we solve each equation for \( Q \):

\[ Q_1 = P_1 - 10 \]
\[ Q_2 = 2(P_2 - 18) \]
\[ Q_3 = 2.5(P_3 - 16) \]

Next, assuming a common market price \( P \), we sum the quantities to get the total market supply \( Q \):

\[ Q = Q_1 + Q_2 + Q_3 \]

Given the structure, it seems we might need to standardize \( P \) for a common expression. However, if we directly add these, we use the prices corresponding to each individual supplier:

\[ Q = (P - 10) + 2(P - 18) + 2.5(P - 16) \]

Simplifying this:

\[ Q = (P - 10) + 2(P - 18) + 2.5(P - 16) \]
\[ Q = P - 10 + 2P - 36 + 2.5P - 40 \]
\[ Q = 5.5P - 86 \]

Therefore, the market supply equation is:

\[ P = \frac{Q + 86}{5.5} \]

Would you like more details or have any other questions?

Here are five more questions you can ask:
1. How do I calculate the equilibrium price in a market?
2. Can you explain the concept of elasticity of demand?
3. What is the difference between marginal cost and marginal revenue?
4. How do you solve a system of linear equations using matrices?
5. Can you help me understand integrals in calculus?

Tip: Always double-check your algebraic manipulations to ensure accuracy in your solutions.

Explore how to calculate the market supply equation by summing individual supply equations and expressing quantities in terms of price. This problem involves algebraic manipulation and is suitable for advanced high school students.

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