A mixed economy is defined by the coexistence of both public and private sectors, where the government and private individuals share the responsibility for economic decisions. This system combines elements of market capitalism with state intervention to address market failures and ensure social welfare, distinguishing it from purely command or purely free-market economies.

The kinked demand curve model, used to explain price rigidity in oligopolistic markets, features a discontinuity in the marginal revenue (MR) curve. Because the demand curve has a 'kink' at the current price, the MR curve drops vertically at that quantity. This gap in the MR curve allows for fluctuations in marginal costs without necessarily changing the equilibrium price, explaining why prices remain stable in oligopolies.

A monopoly exists when there is a single seller in the market with no close substitutes for its product. Because the firm is the sole provider, it faces the entire market demand curve, allowing it significant control over price fixation compared to firms in competitive markets.

In perfect competition, a firm maximizes profit by producing at the quantity where Marginal Revenue (MR) equals Marginal Cost (MC). If MR exceeds MC, the firm can increase profit by producing more; if MC exceeds MR, the firm should reduce production.

The industry supply curve is the horizontal summation of individual firms' marginal cost (MC) curves above their average variable cost. If the marginal costs of all firms increase, the supply curve shifts upward to the left. Conversely, if MC decreases, the supply curve shifts downward to the right, indicating higher supply at each price level.

In perfect competition, there are numerous buyers and sellers, and the product is homogeneous. Because no single firm has sufficient market power to influence the market price, each firm must accept the prevailing market price determined by the intersection of aggregate supply and demand, making them price takers.

In perfect competition, a firm reaches equilibrium when Marginal Cost (MC) equals Marginal Revenue (MR). Additionally, since the firm is a price taker, the price is equal to the Marginal Revenue, which is also equal to the Average Revenue (AR). Therefore, the conditions are MC = MR and MR = AR. Condition 2 is not required for equilibrium, and condition 4 describes the long-run break-even point.

In a monopoly, equilibrium occurs where marginal revenue equals marginal cost. When earning only normal profit, the average cost curve is tangent to the demand curve. The relationship between marginal cost and average cost at this specific output level often results in marginal cost being below the average cost, as the firm operates on the downward-sloping portion of the cost curve.

A natural monopoly occurs when a single firm can supply the entire market at a lower average cost than two or more firms. This is driven by significant economies of scale, high fixed capital costs that create barriers to entry, and limited market size relative to the efficient scale of production, making competition unsustainable.

In monopolistic competition, a firm reaches short-run equilibrium where Marginal Revenue (MR) equals Short-run Marginal Cost (SMC), provided the SMC curve intersects the MR curve from below. Additionally, for the firm to continue production in the short run, the price must at least cover the Average Variable Cost (AVC). This ensures the firm minimizes losses or maximizes profits under existing market constraints.