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Chapter 14 / Partial Equilibrium

14.5 Partial Equilibrium

We’re now — finally! — ready to bring market demand and market supply together.

Market equilibrium occurs when the price is such that the market quantity demanded equals the market quantity supplied.

Formally, a price $p^\star$ is an equilibrium price in a market if:

For example, in the past two sections, we derived the supply and demand functions \(\begin{aligned}S(p) &= N_F \times {\overline K p \over 2w}\\ D(p) &= N_C \times {\alpha m \over p}\end{aligned}\) If we set these two equal to one another, we get \(\begin{aligned}S(p) &= D(p)\\ N_F \times {\overline K p \over 2w} &= N_C \times {\alpha m \over p}\\ p^2 &= {N_C \over N_F} \times {2 \alpha m w \over \overline K}\\ p^\star &= \sqrt{\frac{N_C}{N_F} \times {2 \alpha m w \over \overline K}}\end{aligned}\) Plugging this back into either the demand or supply function gives us the quantity in the market will be \(Q^\star = S(p^\star) = D(p^\star) = \sqrt{N_FN_C\overline K \alpha m \over 2w}\) This looks like a lot of variables! But in fact, what we’re seeing is that we can do all our usual Econ 1 comparative statics just from these expressions:

You can see how each of these effects (and their opposites) play out in the following diagrams. The middle diagram shows market supply and demand; the left diagram shows individual demand, and the right diagram shows individual supply.

Try changing the parameters, and see what happens to the supply or demand curves.

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Next: Equilibrium with Different Consumers and Firms
Copyright (c) Christopher Makler /