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Supposed there are a fixed number of 1000 identical firms in a PC industry, with each producing the same fraction with the same production function

$$q_{i} = \sqrt{K \cdot L}$$

And market demand is given by $Q = 400000 - 100000P$ and $w=r=1$ (arbitrary).

I am having problems finding the long run equilibrium price and quantity. I can solve for MPK and MPL but that just gives me the ratio of inputs used, (i.e. $x=y$). Am I missing some connection between that, $Q$ and $P$?

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    $\begingroup$ You are looking for the long-run equilibrium. Think about what information that might give you... $\endgroup$ – Ubiquitous Jul 28 at 7:54

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