# Does it ever make sense to underproduce as a firm?

The larger the supply, the lower the price. Therefore, the more thneeds you (the firm) produce, the less you'll be able to sell each one for. Traditional sense says that as long as there are people who will buy them, you should always make more thneeds! But given profit is quantity * (selling price - costs), as price drops, you may eventually reach a point where profit decreases the more thneeds you make.

If and when this happens depends on the shape of the supply-demand curve, rather than using the simplified linear ones you learn about in early university economics.

Does this happen? Is there a "supply-induced-price-drop-compensated" ideal quantity to produce to maximize profit?

• While I enjoy Dr. Seuss, I would recommend to just use word quantity instead of that obscure reference. Most people will not get the reference and it does not add any value to the question – 1muflon1 Oct 28 '20 at 19:23
• This is exactly why there is a supply curve. Perhaps you need to understand the idea of disequilibrium in market. More production than equilibrium (intersection of supply-demand curves) means consumers are willing to pay less than what suppliers are willing to accept. So clearly producer will not produce more than equilibrium quantity (even when there is demand). I wouldn't call it underproduce though. Underproduction is often used in a different context; particularly producing less than physical capacity of a firm or even underproducing than static profit maximizing output. – Dayne Oct 29 '20 at 0:21

An interesting case is: should a firm ever produce less than the profit-maximizing output? This could make sense in a dynamic setting: by underproducing in the short run, you might increase future long-run demand. For example, when popular toys like Cabbage Patch Kids and Power Rangers were first released, they were in short supply. Parents went nuts trying to find them, and there was lots of media coverage. Eventually the supply increased; to be honest, I don't know if they raised the price but they could have.

Yes there are cases when it is rational for firm to deliberately 'underproduce'. A trivial example of this is simple monopoly problem. It even works with basic linear demand and would extend to host of other demand functions.

Assume demand is $$q = 100-p$$, assume total cost function is given by $$C(q) = q^2$$

The profit function by monopolist is given by total revenue minus total costs or:

$$\Pi = p(q)q - q^2$$

Solve the demand for price and substitute into the profit to get:

$$\Pi = (100 -q )q - q^2$$

Then maximizing the above profit function yields optimum profit-maximizing quantity:

$$= 100 -2q - 2q = 0 \implies q^* = 25$$

At the quantity $$25$$ the profit would be $$1250$$. The firm could profitably produce even $$26$$ units of the product, in such case firm's profit would be $$1248$$, but as you can see the quantity is equal to $$25$$ is the spot where the profit is maximized. So you can say in this case monopolist is deliberately reducing output just to get more profit. As mentioned above this extends to various other demand functions, only in a special case when demand is perfectly elastic would monopolist produce maximum possible quantity that would still yield at least non-negative profit.

This can also happen outside the monopoly case, however an exhaustive treatment of this topic would be beyond scope of SE. If you want to learn more good textbook for industrial organization is Belleflamme & Peitz (2015). Industrial organization: markets and strategies. Cambridge University Press.

By the verbal description I understand that the OP considers quantity as the driving force here, and also that price depends negatively on it, $$\partial P /\partial Q <0$$. So we consider price as a function of quantity,

$$\pi = P(Q)\cdot Q - C(Q)$$

Maximizing this with respect to quantity, we get the f.o.c in general form

$$\frac{\partial \pi}{\partial Q} = 0 \implies \frac{\partial P}{\partial Q} \cdot Q + P - \frac{\partial C}{\partial Q}=0$$

$$\implies P(Q) = \Big|\frac{\partial P}{\partial Q}\Big|\cdot Q + \frac{\partial C}{\partial Q}.$$

Here is your supply function that always satisfies the f.o.c. for maximum profits, and gives price as a function of quantity (with price in the vertical axis as is customary in this neighborhood). Specify a price function and a cost function, if you want to see something more concrete.

Moreover, it is not difficult to show that the unconstrained profit function is a frontier, and so any constrained imposed or self-imposed on the firm's problem may lead to output lower than the profit-maximizing one. For example, a real-world firm may operate under a budget constraint, or it may has a short-term goal to maintain a minimum level of output (to protect market share). Etc