# General Equilibrium Modelling

I have a question regarding GE modelling. The firm's problem is to: $$\max\pi=pf(k,l)-wl-rk$$

If this is true, we choose $l$ and $k$ to maximize the difference between costs and revenues. This yields the familiar FONCs for $l$ and $k.$ However, in equilibrim, we set the profits equal to 0.

My intuition tells me that after we solve the above problem, the equilibrium condition implies our selecting a price $p$ such that $\pi$ equal $0$ in equilibrium. Is this correct?

• You may have forgotten to add the constraints... Nov 15 '15 at 15:54
• To the best of my knowledge, the profit maximization problem of the firm is an unconstrained one..the duality is with the cost minimization problem which is constrained Nov 15 '15 at 15:58

## 1 Answer

In a typical GE model, price (including wage and rent) is determined by the market clearing condition, which requires that supply equals demand. Specifically,

• labor supplied (determined by household solving utility maximization problem) equals labor demanded (determined by firm's profit maximization problem)
• goods supplied (determined by firm's optimal total production) equals goods demanded (determined by household's consumption and investment decisions)
• capital supplied (household's investment decision) equals capital demanded (firm's optimal choice of $k$)

The zero-profit condition is derived from the assumption of perfectly competitive behavior (or both firms and households are price takers). This condition may contribute to the determination of equilibrium prices. But to say that $p$ is selected to ensure zero-profit of the firm just sounds incorrect.

• Thanks for your response. What does not make sense is the fact that firms both a) maximize profits and b) have 0 profits. How can that be? You cannot simultaneously have for the same function the same set of inputs that both maximizes the objective function and equals 0 Nov 16 '15 at 20:03
• unless of course the function is a constant function or the maximum is at 0 Nov 16 '15 at 20:10
• @ChinG: Several things. First, there is nothing wrong with the maximum profit being zero if the alternative is to earn a negative profit (or loss). The profit here is understood as "economic" profit (where costs are understood as opportunity costs) as opposed to "accounting" profit (which is revenue minus expenditure as appeared in the company's books). Nov 16 '15 at 21:28
• @ChinG: Second, a typical justification for the zero profit condition is the free-entry/exit hypothesis. If there is a market in which firms are making positive profit, other firms will rush in, thereby increasing competition and driving down profit (think of the example of Cournot competition with $n$ firms, and $n\to\infty$). The inflow of new firms will stop when profit is zero. Third, assuming price-taking behavior is partly to simplify the analysis, so that one doesn't have to consider strategic motives of the firms when they are making decisions. Nov 16 '15 at 21:28
• K: thanks a lot for your answers. I think what happens is that the zero profit condition implies that w and r are selected to guarantee that profits equal 0 in equilibrium. Nov 16 '15 at 22:49