Q.Consider a market for wheat in which the demand curve is given by $q_D = 200 - p$ for $0 \le p \le 200$ and $q_D = 0$ for $p > 200$. Assume that the market consists of identical firms and that the supply curve of a single firm is given by $q_S^f = 10 + p$ for $p \ge 20$ and $q_S^f = 0$ for $0 \le p < 20$. With free entry and exit of firms, find the equilibrium price, the equilibrium quantity, and the equilibrium number of firms.

In a market with free entry and exit, firms will enter if there are supernormal profits and exit if there are losses. This process continues until economic profits are driven to zero for all firms. This long-run equilibrium condition implies that the market price ($p^*$) will be equal to the minimum average cost of production for each firm.

The supply curve of a single firm is given by $q_S^f = 10 + p$ for $p \ge 20$ and $q_S^f = 0$ for $0 \le p < 20$. The condition $q_S^f = 0$ for $p < 20$ indicates that firms will not supply any quantity if the price falls below $20$. This minimum price of $p=20$ represents the minimum average cost (and minimum average variable cost in the short run, and minimum average cost in the long run for zero economic profit). Therefore, the equilibrium price in this market with free entry and exit is $p^* = 20$.

1. Equilibrium Price ($p^*$):

   With free entry and exit, the equilibrium price is determined by the minimum point of the average cost curve of the firms. From the given firm's supply curve, $q_S^f = 0$ for $p < 20$, meaning firms will only supply at prices $p \ge 20$. Thus, the minimum price at which firms operate is $p=20$.

   $p^* = 20$

2. Equilibrium Quantity ($q^*$):

   Substitute the equilibrium price into the market demand curve:

   $q_D = 200 - p$

   $q^* = 200 - 20$ …

In a perfectly competitive market, the concept of equilibrium is central. It represents a state where there is no inherent tendency for change, as both consumers and producers are satisfied with the prevailing price and quantity. When we introduce the condition of "free entry and exit" for firms, we are specifically looking at the long-run equilibrium.

The economic intuition behind free entry and exit is crucial: if firms in the market are making positive economic profits, new firms will be attracted to enter the market. This entry increases the total market supply, which in turn drives down the market price. Conversely, if firms are incurring economic losses, some existing firms will exit the market. This exit reduces total market supply, pushing the market price up. This process of entry and exit continues until economic profits are driven to zero. Zero economic profit means that firms are earning just enough to cover all their costs, including the opportunity cost of capital and entrepreneurship. This condition is met when the market price equals the minimum point of the firm's long-run average total cost (LRATC) curve.

Let's find the equilibrium price, quantity, and number of firms:

1. Determine the long-run equilibrium price ($p^*$): With free entry and exit in a perfectly competitive market, the long-run equilibrium price will settle at the minimum average total cost (ATC) of a firm. The individual firm's supply curve is given by $q_S^f = 10 + p$ for $p \ge 20$ and $q_S^f = 0$ for $0 \le p < 20$. The condition $q_S^f = 0$ for $p < 20$ indicates that the firm will not produce if the price falls below $20$. This price of $20$ represents the minimum point of the firm's average cost curve (specifically, the minimum average variable cost in the short run, and the minimum average total cost in the long run for free entry/exit). Therefore, the equilibrium price in this market is:

2. Determine the equilibrium quantity supplied by each firm ($q_f^*$): Substitute the equilibrium price $p^* = 20$ into the individual firm's supply curve: …