# Calculating equilibrium in a cobb-douglas long run, perfect competition scenario

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 $$P$$?

• You are looking for the long-run equilibrium. Think about what information that might give you... – Ubiquitous Jul 28 '19 at 7:54