Domain: Humanities and Social Sciences — Economics
Target concept: Economies of scale: the average cost curve decreases as output increases.

Video generation prompt: The figure shows a coordinate system in which the horizontal axis represents output and the vertical axis represents average cost. A curve is plotted in the figure, illustrating how costs change with increasing output under conditions of economies of scale.

Evaluation guide:
Target concept: Economies of scale defined mechanistically as the reduction in average cost per unit resulting from increased output, driven by indivisible fixed inputs and operational efficiencies. Minimum assumptions: (i) cost structure includes fixed + variable components; (ii) output is exogenous and scalable; (iii) technology and input prices are constant. Expected phased storyline: (1) Static setup: blank coordinate plane appears; (2) Axis revelation: "Output" (x) and "Average Cost" (y) labels materialize with directional arrows; (3) Curve genesis: a smooth, continuous line emerges left-to-right, visibly descending (higher AC at low Q, lower AC at high Q); (4) Final state: fully rendered curve with no ambiguity. Visibility constraints: front-facing, orthographic 2D view; no occlusion; all labels and curve must be legible at native resolution; causal transition must be temporally ordered (axes → curve → confirmation of descent) and perceptually unambiguous (monotonic slope + axis semantics alone suffice for verification).

Manual:
I. Basic Demonstration Information
Demonstration Title: Economies of Scale — Average Cost Curve Demonstration
Subject: Economics - Microeconomics - Production and Costs
Demonstration Purpose: To visually demonstrate that under economies of scale, the average cost (AC) curve declines as output increases; to reinforce the inverse quantitative relationship between output level and per-unit cost; and to train recognition of the characteristic downward-sloping segment of the AC curve.

II. Demonstration Carrier/Equipment
Core Carrier: Animated 2D coordinate plot (digital, vector-based)
Auxiliary Equipment: Clean white background; sans-serif, high-contrast font (e.g., Arial Bold); optional subtle animation engine for progressive curve drawing.

III. Demonstration Content Description
Layout: Full-screen Cartesian plane centered horizontally and vertically. Horizontal axis labeled "Output (Q)" with rightward arrow; vertical axis labeled "Average Cost (AC)" with upward arrow. Origin at bottom-left corner.
State Control: Axes render first and remain static. Curve draws progressively from left (low Q, high AC) to right (high Q, low AC) over 6–8 seconds — smooth, continuous, monotonic descent.
Comparison Baseline: No competing curves (e.g., no MC or AVC overlay); no grid distortion; curve exclusively represents AC under pure economies of scale (no U-turn or rising segment).

IV. Observation of Core Phenomena
Expected Phenomenon: A single, unbroken, downward-sloping curve starting in upper-left quadrant and ending in lower-right quadrant.
Expected Screen: Clean, minimal, high-contrast plot. No legends, titles, or decorative elements beyond axis labels and curve.
Visual Verification Features:
– Horizontal axis must be labeled "Output" (or "Q") and extend rightward;
– Vertical axis must be labeled "Average Cost" (or "AC") and extend upward;
– Curve must be smooth, continuous, and strictly decreasing (no flat, rising, or oscillating portions);
– Curve must originate above and terminate below the visual centerline — confirming declining magnitude;
– No secondary objects (e.g., data points, arrows, annotations) unless explicitly part of core verification (e.g., optional small arrow + "Economies of Scale" near curve midpoint).

V. Summary of Key Knowledge Points and Principles
Core Concept Definition: Economies of scale occur when increased production volume leads to lower average cost per unit, typically due to spreading fixed costs and operational efficiencies.
Principle Visualization: The downward-sloping segment of the AC curve is the graphical signature of economies of scale — a direct, observable manifestation of the inverse functional relationship AC = f(Q), where d(AC)/d(Q) < 0 in this range.

VI. Demonstration Precautions
– Avoid any rising, flat, or non-monotonic curve segments — these represent diseconomies or constant returns, violating the target concept.
– Do not introduce extraneous elements (e.g., marginal cost curve, firm boundaries, or factory icons) that distract from the pure AC–output relationship.
– Ensure axis labels are unambiguous: "Output", not "Quantity" or "Units"; "Average Cost", not "Cost" or "Price".
– Animation must proceed left-to-right only; no backtracking, fading, or morphing.

Prompt Grounding rubric:
level_1: No coordinate system, axes, or curve of any kind appears; the video shows something unrelated to a plot of output versus cost (e.g., a bar chart, a photograph, plain text, or abstract shapes) with no attempt to depict the relationship at all.
level_2: A coordinate system is drawn, but its axis labels are missing entirely or are clearly wrong for this concept (e.g., the horizontal axis reads "Time" or "Price" instead of "Output", the vertical axis reads "Revenue" or "Total Cost" instead of "Average Cost"); any curve shown trends flat or rises overall rather than heading downward from left to right.
level_3: Coordinate system has axes in the correct orientation (horizontal = output, vertical = average cost), but at least one axis label is missing, misspelled, or hard to read; a single curve is drawn that trends downward overall from left to right across the plotted output range (the curve's precise shape and smoothness are judged separately, not here).
level_4: Both axes are present with clear, correctly spelled labels ("Output" on the horizontal axis, "Average Cost" on the vertical axis) and visible tick marks; a single curve runs from the upper-left toward the lower-right of the plot; only a minor stylistic shortfall remains, such as missing gridlines, uneven tick spacing, or no accompanying text near the curve.
level_5: Clean, fully labeled Cartesian plane with bold, legible "Output" and "Average Cost" axis titles, evenly spaced tick marks, and optional faint gridlines; a single curve of consistent line weight runs from upper-left to lower-right; no extraneous text, watermarks, stray marks, or clutter anywhere in frame; an optional small annotation (e.g., an arrow with the words "Economies of Scale") sits near the curve without obscuring it.

Scientific and Causal Correctness rubric:
level_1: The curve is flat, rises with output, or looks scattered/random, showing no relationship, or the opposite relationship, between output and average cost; nothing conveys that producing more lowers the cost per unit.
level_2: The curve trends downward comparing its start to its end, but is not monotonic along the way (e.g., it rises then falls, or plateaus then drops sharply partway through), so the depicted relationship contradicts a continuous decline in average cost as output rises.
level_3: The curve decreases monotonically from left to right across the whole plotted range, but its shape does not resemble a typical declining average-cost curve under economies of scale, for example a straight-line descent rather than the expected concave, ever-flattening decline as fixed costs spread over more units.
level_4: The curve decreases monotonically with a concave shape (steep at low output, flattening as output grows), consistent with fixed costs being spread over increasingly many units; the only shortfall is a minor omission, such as no numeric output/cost values shown or no explicit cue (arrow, label, or callout) tying the descent to "more units produced, lower cost per unit."
level_5: The curve's shape and trajectory fully embody economies of scale: it descends monotonically with concave, ever-flattening curvature reflecting fixed costs spread over more units, matching the declining segment of a standard average-cost curve; if a moving marker or numeric readout is shown (e.g., "Q=10, AC=$8" moving to "Q=50, AC=$4"), the values themselves decrease as output rises with no contradicting numbers; nothing in the scene suggests a rising, flat, or discontinuous cost relationship.

Spatiotemporal Consistency rubric:
level_1: Axes are spatially incoherent (e.g., the vertical axis is drawn horizontally, or the origin sits in the wrong place); the curve is disconnected from the axes; the plot jumps or flickers suddenly; the sequence of events makes no sense (e.g., the curve draws backward, labels appear only after the curve is finished, or the axes fade in partway through the animation).
level_2: Axes are roughly perpendicular but placed oddly (e.g., the vertical axis sits on the right side, or the origin is off in a corner); the curve begins drawing before the axes have finished appearing; the output or cost units visibly rescale mid-animation (an axis stretches or compresses); the whole plot noticeably stutters or drifts in position during the animation.
level_3: Axes stay stable and correctly placed for the whole video; the curve draws sequentially from left to right, but its pace is uneven (e.g., it pauses partway through, then rushes to finish); tick spacing looks slightly irregular on one axis; the overall framing holds steady with no drift.
level_4: The composition stays stable and centered throughout; the axes finish appearing before the curve starts animating; the curve draws left-to-right at a visibly steady, even pace with consistent line thickness; tick marks and axis labels stay sharp and in place; only a very minor cosmetic slip remains, such as a tick label momentarily touching the axis line or one gridline looking thinner than the rest.
level_5: Axes appear fully drawn and hold still from the first frame onward; the curve's motion looks smooth and continuous to the eye, with no visible stutter, backward movement, warping, or sudden change in scale; all labels stay crisp and correctly positioned for the entire video; the camera framing and perspective (frontal, flat-on) never shifts.