The problem describes a market with 100 identical firms. Each firm has a short-run total cost (STC) function given by $STC = q^2 + q + 10$, which leads to a marginal cost (MC) function of $MC = 2q + 1$. The market demand is given by $QD = 1050 - 50P$. The goal is to determine the individual firm's production quantity in equilibrium.

1. Problem Description

The problem describes a market with 100 identical firms. Each firm has a short-run total cost (STC) function given by $STC = q^2 + q + 10$, which leads to a marginal cost (MC) function of $MC = 2q + 1$. The market demand is given by $QD = 1050 - 50P$. The goal is to determine the individual firm's production quantity in equilibrium.

2. Solution Steps

First, we need to derive the market supply curve. Since all 100 firms are identical, the market supply curve is simply 100 times the individual firm's supply curve. A firm's supply curve is its marginal cost curve above its minimum average variable cost. In this case, the MC is always above the AVC since AVC goes to zero. A firm produces where price equals marginal cost (P = MC). So, for each firm:

$P = 2q + 1$

Solving for q, we get the individual firm's supply curve:

$q = (P - 1)/2$

Since there are 100 firms, the market supply (QS) is:

$QS = 100 * q = 100 * (P - 1)/2 = 50(P - 1) = 50P - 50$

Next, we set market supply equal to market demand to find the equilibrium price:

$QD = QS$

$1050 - 50P = 50P - 50$

$1100 = 100P$

$P = 11$

Now that we have the equilibrium price, we can plug it back into the individual firm's supply curve to find the quantity produced by each firm:

$q = (P - 1) / 2$

$q = (11 - 1) / 2$

$q = 10 / 2$

$q = 5$

3. Final Answer

The individual firm will produce 5 units.