# Till what point do firms enter a market?

Hal Varian states that for a firm to enter an industry, the condition should be such that the price that the firm is charging is slightly above (p') the market price (p*) in a perfectly competitive industry, to make some form of economic profit.

I have two questions here:

1. How can existing firms charge more than the market sets the price? Assuming that firms are perfectly competitive and hence, price-takers?

2. He also mentions that at any price p'< p*, firms will not enter because there will be no economic profit (which is logical and will thus lead to exit). However, will firms enter if there is a condition of normal profits? (i.e p' = p*, and thus profits = 0)

If it helps, I'm attaching a related figure here. Please do correct me if I am mistaken in my understanding of the topic.

• Commented Aug 1 at 21:11

How can existing firms charge more than the market sets the price? Assuming that firms are perfectly competitive and hence, price-takers?

They do not. The graph is an abstraction. What the graph visualizes is a temporary equilibrium where price is p'. Note p' is the market price. It is is just not the same market price in perfectly competitive industry without entry costs because in short run the barrier to entry also reduces competition.

Firms are price takers, but the price they take is the price at a point where supply intersects demand. The entry costs do not allow supply to expand as much to the right as in a contrafactual without them.

He also mentions that at any price p'< p*, firms will not enter because there will be no economic profit (which is logical and will thus lead to exit). However, will firms enter if there is a condition of normal profits? (i.e p' = p*, and thus profits = 0)

Yes firms will enter when normal economic profits = 0. Note normal economic profit = 0 is not the same as accounting profit = 0. For example, if you are good manager who would be expected to earn 1 million euros when employed as CEO of some company, then at 0 normal profit you need to get 1 million euros of accounting profit per year since that is your opportunity cost.

Hence, at zero economic profit person is already perfectly compensated for running the business. It is not the same as having no accounting profit. Zero economic profit means you are already compensated sufficiently for all efforts, disutility and just generally all explicit or implicit costs, even if the costs are psychological and subjective.

• Can you please explain your sentence "The entry costs do not allow supply to expand as much to the right as in a contrafactual without them."? I am not sure where you are getting any information on entry costs from Varian's graph. Commented Jul 31 at 15:26
• You seem to be using the OP's phrase "normal profit" for a paragraph when you mean "economic profit". You use "economic profit" in the next paragraph, but you never equate the two or explain the difference (if there are any). Commented Jul 31 at 15:28
• @Giskard regarding the first one I got that from the context of a question, maybe I am misreading it but I saw similar graph in one of the varian’s textbook when the discussion was between the short and long run where in short run fixed costs create barrier to entry. If that’s wrong then I will correct it but based on what’s in the question I believe this was what it refers to OP doesn’t provide full citation so I admit I am doing little bit guess work here. Regarding 2 I adjusted that
– 1muflon1
Commented Jul 31 at 17:43
• I was thinking a bit the other day, and you can indeed glean a firm's fixed costs (entry costs?) from this graph; it is the area between $S_1$ and the horizontal line at $p^*$. Image Commented Aug 4 at 15:19

I think that @1muflon1's answer is quite correct.

Setting up a small model can perhaps make some concepts a little clearer. The model is not general. However, I think it will illustrate what Hal Varian aims at in the chapter referred to.

The chapter is available here with the graph illustrated on page 417.

Consider a Cobb-Douglas production technology with constant returns to scale with output given by the production function

\begin{align} F(L,K) = \left(\frac{L}{\alpha}\right)^{\alpha}\left(\frac{K}{1-\alpha}\right)^{1-\alpha}. \end{align} In the long run, the firm can alter labor and capital. The long-run cost minimization problem therefore minimizes the cost $$wL + rK$$ with respect to $$K$$ and $$L$$ subject to $$F(K, L)\geq Y$$. The solution to this problem is

\begin{align} C(Y) = (w^\alpha r^{1-\alpha}) \times Y, \end{align} implying that the long-run average cost (LRAC) and long-run marginal cost (LRMC) are equal to the unit costs \begin{align} LRAC = LRMC = w^\alpha r^{1-\alpha}. \end{align} Under perfect competition with free entry the equilibrium price $$p^\star = LRAC = LRMC = w^\alpha r^{1-\alpha}$$.

In the short run capital is fixed and I assume that each firm uses $$\bar K$$ units of capital. As a result, each firm has a fixed cost equal to \begin{align} F = r\bar K. \end{align} In the short run firm minimizes cost with respect to $$L$$. Define $$\beta(K) = \left(\frac{K}{1-\alpha}\right)^{1-\alpha}$$ and invert the production function in $$L$$ to get that \begin{align} L = \alpha \left(\frac{Y}{\beta(K)}\right)^{1/\alpha}, \end{align} which implies that the short-run cost function is given as \begin{align} SC = \alpha w \left(\frac{Y}{\beta(K)}\right)^{1/\alpha} + F = \gamma Y^{1/\alpha} + F, \end{align} with $$\gamma:=\alpha w/\beta(K)^{1/\alpha}$$.

In the short run, the firms act competitively and will therefore maximize profit while taking the price as given. They therefore solve the problem \begin{align} \max_{Y_i} \ \ \ p' Y_i - \left[\gamma Y_i^{1/\alpha} + F\right], \end{align} implying that the price will be equal to the short-run marginal cost \begin{align} p' = \frac{\gamma}{\alpha} Y_i^{\frac{1-\alpha}{\alpha}}, \end{align} and the individual firm will therefore supply \begin{align} Y_i = \left(\frac{\alpha}{\gamma} p' \right)^{\frac{\alpha}{1-\alpha}}. \end{align} I then assume that firms use the same production technology and identical amounts of capital - hence for all firms $$K=\bar K$$ - such that the total short-run supply is simply given as \begin{align} S(p') = N Y_i(p') = N \left(\frac{\alpha}{\gamma} p' \right)^{\frac{\alpha}{1-\alpha}}. \end{align} Finally, I assume that demand is simply given as \begin{align} D(p') = \frac{I}{p'}. \end{align} The supply and demand curves can now be plotted for different values of $$N$$ corresponding to the number of firms. The choice of parameter values can be read of from the r-code used to generate the plot.

Furthermore, the short-run equilibrium price is given as the solution to $$D(p') = S(p')$$ which results in the short-run equilibrium price \begin{align} p^\star_{N} = \left(\frac{I}{N}\right)^{1-\alpha} \left(\frac{\gamma}{\alpha}\right)^{\alpha}, \end{align} which can then be reinserted into the individual short-run supply to find the individual firm supply in equilibrium

\begin{align} Y^\star_{i,N} = \left(\frac{I}{N} \times \frac{\alpha}{\gamma}\right)^{\alpha} . \end{align} Finally, reinserting short-run equilibrium price and individual supply into the profit function the profit in short-run equilibrium is found to be \begin{align} \Pi^\star_{i,N} = (1-\alpha) \left(\frac{I}{N} \right)-F. \end{align}

Firms will do entry as long as \begin{align} \Pi^\star_{i,N} = (1-\alpha) \left(\frac{I}{N} \right)-F > 0, \end{align} implying that equilibrium number of firms is $$N^\star = (1-\alpha) \frac{I}{F}$$.

In the numerical example, I let $$\bar K = 1$$ and $$r=1$$ so fixed cost $$F = r \bar K = 1$$. The income spent by consumers on the market $$I=100$$ and $$\alpha=0.3$$ such that the equilibrium number of firms is $$N^\star = 70$$.

w <- 1
r <- 1

alpha <- 0.3
K_bar <- 1
beta <- (K_bar/(1-alpha))^(1-alpha)
gamma <- alpha*w/beta^(1/alpha)

I <- 100

# Calculate fixed cost
F <- r*K_bar
p_star <- r^(1-alpha) * w^alpha

demand <- function(p)
{
out <- I/p
return(out)
}

supply <- function(p)
{
k <- (alpha/gamma)^(alpha/(1-alpha))
out <- k*p^(alpha/(1-alpha))
return(out)
}

p <- seq(0,15,length.out=100)
plot(demand(p),p,xlim=c(0,150),type="l")
points(5*supply(p),p,col="red",type="l")
points(15*supply(p),p,col="red",type="l")
points(25*supply(p),p,col="red",type="l")
points(35*supply(p),p,col="red",type="l")
points(45*supply(p),p,col="red",type="l")
points(55*supply(p),p,col="red",type="l")
points(70*supply(p),p,col="red",type="l",lwd=2)
abline(h=p_star,col="blue",lwd=2)

# Long run output
Y_bar <- (alpha*F/((1-alpha)*gamma))^alpha
P_bar <- (gamma/alpha)*Y_bar^((1-alpha)/alpha)
N <- I/(P_bar*Y_bar)
abline(v=Y_bar*N,lwd=2)

n_vec <- c(5,15,25,35,45,55,70)

p_N_star <- function(N)
{
out <- ((I/N)^(1-alpha))*((gamma/alpha)^alpha)
return(out)
}

y_N_star <- function(N)
{
out <- ((I/N)*(alpha/gamma))^alpha
return(out)
}

prices <- p_N_star(n_vec)
quantities <- y_N_star(n_vec)*n_vec

points(quantities,prices,pch=20)

profit <- function(N)
{
out <- (1-alpha)*(I/N) - F
return(out)
}

profit(n_vec)