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In former articles, we were introduced to Cost Minimization and Price Elasticity. In this article, we will take a look at Supply Curves for companies and derive the Market Equilibriums — both in the short and long run.
Deriving the Supply Curve
We can first start by stating our conditions. We imagine that we have a situation where we have ‘n’ distinct companies. They all take a price, p. They all, also, have the following cost function:
where we have x > 0 and F > 0. Here, ‘F’ is simply the fixed costs — they have to be paid whether the company is producing anything or not. Since we will need it later, we can also give the demand function:
We can now derive the Supply Curve, y(p). First, we will need to derive the marginal costs, which is simply done by deriving the cost function with respect to y:
We then use the condition that p ≥ MC(y), which then gives us the following condition:
We then simply solve for y, which will then give us the supply curve:
Since we have now derived the supply curve for a single company, we can also do it for all ’n’ companies. This is given by the following:
Deriving the Market Equilibrium
We have now derived the supply function. We can now find the Market Equilibrium. What does this mean? It simply means when the supply of all n companies is equal to…
