Firms in Factor Markets and Production Economics

Flashcards covering key vocabulary and mathematical concepts for microeconomic production functions, cost-minimization strategies, and scale economics.

Production Function

The relationship showing the maximum achievable quantity of output ($q$) from a given quantity of inputs, typically represented as $q = f(L, K)$, where $L$ is labour and $K$ is capital.

Average Product of Labour ($AP_L$)

A global measure of productivity equal to total output divided by the total quantity of labour input ($AP_L = \frac{q}{L}$).

Marginal Product of Labour ($MP_L$)

A local measure of productivity representing the increase in output resulting from a very small change (one additional unit) in the quantity of labour, expressed as the partial derivative of the production function: $MP_L = \frac{\Delta q}{\Delta L}$.

Law of Diminishing Returns

The phenomenon where, from a certain turning point, the marginal product (additional returns) of a production factor starts to decrease as the amount of that factor increases.

Production Isoquant

A curve showing all various combinations of labour ($L$) and capital ($K$) that, when used optimally, produce a specific, given level of output.

Axiom of Transitivity

An isoquant property stating that if a producer prefers input mix A over B, and B over C, they must prefer A over C; this implies that isoquants from the same producer cannot intersect.

Marginal Rate of Technical Substitution (MRTS)

The slope of the tangent to the isoquant at a specific point, representing the ratio at which inputs can be substituted for one another while maintaining the same level of output ($MRTS = \frac{\Delta K}{\Delta L} = - \frac{MP_L}{MP_K}$).

Perfect Substitutes (Production)

Inputs for which the $MRTS$ remains constant regardless of the combination used, resulting in linear isoquants.

Leontief Technology

A production process that uses inputs in fixed proportions, meaning the factors are perfect complements; this results in L-shaped isoquants where $MRTS$ changes from infinity to zero at the vertex.

Returns to Scale

A measure of how total production evolves given an equal proportional increase ($\lambda > 1$) in all production factors ($L$ and $K$).

Increasing Returns to Scale

A situation where a proportional increase in inputs leads to a more than proportional increase in output ($TP(\lambda L, \lambda K) > \lambda \cdot TP(L, K)$).

Decreasing Returns to Scale

A situation where a proportional increase in inputs leads to a less than proportional increase in output ($TP(\lambda L, \lambda K) < \lambda \cdot TP(L, K)$).

Cobb-Douglas Production Function

A functional form $q = A L^{\alpha} K^{\beta}$, where $A$ is total factor productivity, and the sum $\alpha + \beta$ determines if there are increasing, constant, or decreasing returns to scale.

Isocost Curve

A curve representing all combinations of labour ($L$) and capital ($K$) that cost the firm the same total amount ($TC$), given the price of labour ($w$) and capital ($r$), defined by $K = \frac{TC}{r} - (\frac{w}{r}) L$.

Cost-Minimizing Input Combination

The equilibrium point where the isoquant is tangent to the lowest possible isocost line, occurring where $MRTS = \frac{w}{r}$ or $\frac{MP_L}{w} = \frac{MP_K}{r}$.

Substitution Effect

The change in input mix that occurs when the relative price of an input changes (e.g., labor becomes more expensive), leading the firm to replace that input with the relatively cheaper alternative (e.g., capital) to maintain the same output level.

Expansion Path

A curve describing how the optimal, cost-minimizing combination of production factors changes as a company increases its desired output level.

Economies of Scale

A condition where the long-run average cost falls as the quantity of output increases, often caused by specialization or the spreading of high fixed costs.

Diseconomies of Scale

A condition where long-run average costs rise as output increases, typically due to coordination and communication problems inherent in large organizations.