Production Theory

Drag the worker slider to move simultaneously on both panels. The top panel draws a tangent line on the TP curve (whose slope is MPL); the bottom panel lights up the corresponding MPL point. This makes the "MPL = slope of TP" relationship viscerally clear. Notice that as you increase the number of workers, the marginal product of labor falls -- this is the Law of Diminishing Marginal Product: each additional worker adds less to total output than the previous one (assuming capital is held fixed).

Compare three production technologies side by side: Cobb-Douglas (smooth convex curves), Perfect Substitutes (straight lines), and Leontief / Perfect Complements (right-angle L-shapes). Toggle between Isoquant mode (firm -- axes L and K) and Indifference Curve mode (consumer -- axes X and Y). The math is identical; only the economic interpretation changes. Drag the red dot on the Cobb-Douglas panel to see how MRTS changes along a curve.

Drag the point along the isoquant Q = K^0.5L^0.5. As you move right (more L, less K), the annotation updates: "At this point, 1 worker replaces X machines." The tangent line redraws and MRTS = K/L updates in real time.

The same Cobb-Douglas function Q = K^aL^b can simultaneously exhibit diminishing MPL AND increasing returns to scale. Left panel: hold K fixed, vary L and watch MPL fall. Right panel: scale both K and L proportionally and watch output more than double.

A ray from the origin cuts through three isoquants (Q = 1, 2, 4). Under CRS the intersection points are equally spaced; under IRS they bunch up; under DRS they spread out. Type in exponents a and b and watch the spacing animate live.

Two fundamentally different actions can change how a firm produces. Pressing "Substitute Inputs" moves the production bundle along the existing isoquant - technology unchanged. Pressing "Improve Technology" shifts the entire isoquant inward - fewer inputs can now produce the same output.

The consumer and the firm face mathematically identical optimisation problems. Left: indifference curve, MRS, budget line. Right: isoquant, MRTS, isocost line. Moving the slider shifts the reference curve on both sides simultaneously.

Set A, a, b using sliders. Live outputs: (1) isoquant map with spacing, (2) CRS/IRS/DRS verdict, (3) MPL and MPK evaluated at (K, L), (4) MRTS at that point. The scale-by-lambda slider directly tests the returns-to-scale definition.

A bakery has a fixed number of machines (K fixed). Hire workers one at a time and watch TP, MPL, and running wage cost update. At some point MPL turns negative and the simulator refuses the hire. Optionally buy a new machine to shift the TP curve upward.

A production function appears. Predict the isoquant shape before it renders, then check if you are right. Covers all three types: smooth convex (Cobb-Douglas), straight line (linear / perfect substitutes), and L-shaped (Leontief / fixed proportions).