Domain: Humanities and Social Sciences — Economics
Target concept: Marginal cost curve characteristics: U-shaped, decreasing first and then increasing.

Video generation prompt: The figure shows a coordinate axis, with the horizontal axis representing quantity and the vertical axis representing cost. A marginal cost curve is plotted on the coordinate axis, and the marginal cost point A is labeled.

Evaluation guide:
Target concept: Marginal cost (MC) is the incremental cost of producing one additional unit; its U-shaped pattern reflects the transition from increasing efficiency (falling MC) to diminishing returns (rising MC). Minimum MC (point A) is the pivotal inflection where production efficiency peaks before decline. Expected phenomena storyline: (1) Coordinate system appears: axes labeled ‘Quantity’ (x) and ‘Cost’ (y); (2) U-shaped curve draws left-to-right, visibly descending then ascending, with smooth curvature and no kinks; (3) Point A materializes precisely at the curve’s minimum, confirmed by geometric alignment and functional vertex consistency. Visibility constraints: All elements must be legible at 1080p without zoom; no occlusion; point A must be unambiguously *on* the curve (not floating or axis-bound); causal transitions must be temporally ordered (axis → curve → point A) and visually reinforced (e.g., curve descent/ascension aligned with textbook economic narrative).

Manual:
I. Basic Demonstration Information
Demonstration Title: Marginal Cost Curve U-Shape Demonstration
Subject: Economics - Microeconomics - Production Costs
Demonstration Purpose: To visually demonstrate the defining U-shaped characteristic of the marginal cost (MC) curve — decreasing initially due to increasing efficiency, then increasing due to diminishing marginal returns — using a standard Cartesian coordinate system with quantity on the x-axis and cost on the y-axis; to identify and label a representative marginal cost point A on the curve for conceptual anchoring.

II. Demonstration Carrier/Equipment
Core Carrier: Static SVG-rendered coordinate plane (1920×1080, high-DPI compatible)
Auxiliary Elements: Axis labels (‘Quantity’ centered below x-axis, ‘Cost’ rotated 90° beside y-axis), gridlines (light gray, 0.5pt), U-shaped blue curve (stroke #1E3A8A, 2pt), labeled point A (red circle ●, radius 6px, bold black ‘A’ label, font size 16pt, positioned on curve near minimum).

III. Demonstration Content Description
Layout: Full-screen coordinate system centered horizontally and vertically. X-axis spans 0–100 units (evenly spaced ticks), y-axis spans 0–120 units. Curve starts at (5, 100), descends smoothly to minimum near (45, 35), then rises to (95, 110). Point A is placed at (45, 35) — the local minimum — with precise coordinates matching curve function.

IV. Observation of Core Phenomena
Expected Screen: Clean, minimalist academic diagram. No extraneous icons, legends, or animations beyond core elements. Background white (#FFFFFF), axis lines black (#000000, 1.5pt), gridlines #E2E8F0.
Visual Verification Features:
– Shape: Curve must be unmistakably U-shaped — concave up overall, with clear downward slope left of minimum and upward slope right of minimum.
– Labels: ‘Quantity’ and ‘Cost’ must be present, correctly oriented, and legible at native resolution.
– Point A: Must be *on the curve*, not above/below it; circular marker must be filled red (#DC2626) with sharp edges; ‘A’ label must be black, sans-serif, horizontally aligned, and within 8px of marker center.
– Consistency: All elements retain fixed spatial relationships — no scaling, shifting, or opacity changes during observation.

V. Summary of Key Knowledge Points and Principles
Core Concept Definition: Marginal cost (MC) is the additional cost incurred by producing one more unit of output. Its U-shape arises from two opposing forces: (1) initial falling MC due to specialization and spreading fixed costs, and (2) eventual rising MC due to diminishing marginal returns to variable inputs.
Principle of Visual Recognition: The U-shape is the *diagnostic visual signature* of MC in standard short-run cost theory. Point A serves as an anchor to locate the minimum MC — a critical point where MC intersects average variable cost (AVC) and signals optimal capacity utilization threshold.

VI. Demonstration Precautions
– No decorative elements (e.g., arrows, shading, background images) permitted — strict adherence to textbook-style schematic.
– Font must be system-safe (e.g., ‘Segoe UI’, ‘Helvetica Neue’, fallback to ‘sans-serif’).
– Curve must be mathematically plausible: defined by quadratic function MC(q) = aq² − bq + c (a > 0) ensuring true convexity.
– Point A must correspond to vertex of parabola (q = b/2a), verified numerically.
– Video duration: exactly 10 seconds — 2s axis reveal, 5s curve draw (left→right, easing), 3s static hold with point A pulsing gently (1.2x scale, 0.5s period).

Prompt Grounding rubric:
level_1: No coordinate axes are drawn at all; or the axes are unlabeled and could represent anything; or no curve is drawn; or point A is never shown; or the image shows something unrelated entirely (e.g. a bar chart, a photograph, or plain text).
level_2: Some kind of axes and a curve appear, but the axis labels are wrong or missing (e.g., the horizontal axis is labeled 'Time' instead of 'Quantity', or the vertical axis is labeled 'Price' instead of 'Cost'); the curve is a straight line, a curve that only rises, a curve that only falls, or an upside-down U rather than a right-side-up U; point A is missing or placed somewhere with no visible relation to the curve (e.g., floating in empty space).
level_3: The horizontal axis is labeled 'Quantity' and the vertical axis is labeled 'Cost' (even if the text is small or the tick marks lack units); a curve is drawn that goes down and then up, though the dip may be shallow or the turn from falling to rising may look abrupt rather than smoothly rounded; point A is labeled somewhere on screen but sits off the curve itself or at an odd spot like the axis origin or the very top of the y-axis.
level_4: Everything required for the 3-point level is present, and in addition: both axis labels are clearly legible, with tick marks or gridlines visible; the U-shaped curve is smooth, clearly falling and then clearly rising, with one identifiable low point; point A sits directly on the curve, though its position may look slightly off from the true lowest point, or it may lack a marker/label that sets it apart from the rest of the curve.
level_5: Everything required for the 4-point level is present, and in addition: the axis labels 'Quantity' (horizontal) and 'Cost' (vertical) are bold and easily readable with evenly spaced scale ticks; the U-shaped curve is smooth, dips to a clear minimum, and rises again on both sides in a shape consistent with a real marginal-cost curve; point A sits exactly on the curve, marked with a distinct circular marker plus a clear 'A' label (in a color that stands out against the curve, such as red or black, and sized comparably to the axis labels), placed unambiguously along the curve rather than at an axis intercept or the frame's edge.

Scientific and Causal Correctness rubric:
level_1: The graph shown has nothing to do with a marginal cost curve, e.g., it looks like a supply-and-demand diagram or an average-cost curve instead; the curve's shape contradicts the theory (e.g., it only ever decreases); or point A is described/positioned as something other than a cost minimum (e.g., labeled as a maximum or a total-cost figure).
level_2: The curve looks roughly like it could be a cost curve, but it violates the basic marginal-cost pattern by only ever rising or only ever falling across its whole length; or point A sits at the highest point of the curve or right where the curve meets an axis, rather than anywhere near the dip; there is nothing to suggest point A is meant to mark the U-shape's turning point.
level_3: The curve visibly falls and then rises, matching the 'decreasing then increasing' description of marginal cost; point A sits on the curve somewhere in the vicinity of the dip; however nothing in the video especially highlights why that particular point matters (it is simply a labeled dot on the curve, with no other cue tying it to the change from falling to rising).
level_4: Everything required for the 3-point level is present, and in addition: the curve's fall-then-rise pattern reads clearly as the standard marginal-cost story (costs coming down, then going back up), and point A is placed at or very near the actual lowest point of the curve, correctly representing the minimum marginal cost, without needing any added icons, arrows, or captions to make the point; the curve's own shape and point A's position are enough to convey the economics correctly.
level_5: Everything required for the 4-point level is present, and in addition: point A sits exactly at the curve's true minimum with no visible offset, and the entire U-shape is smooth and unambiguous enough that a viewer familiar with a standard marginal-cost diagram would immediately recognize the falling segment as reflecting improving efficiency and the rising segment as reflecting diminishing returns, using only the curve's shape and point A's exact placement; no added text, icons, or callouts are shown or needed to make this reading correct.

Spatiotemporal Consistency rubric:
level_1: The axes, the curve, or point A appear and then vanish and reappear at some point in the clip; the axis scale or the curve's shape suddenly jumps to something different between two frames with no drawing motion in between; the on-screen labels change wording partway through (e.g., 'Cost' turns into a dollar sign); or point A jumps to a different spot on the curve with no visible movement getting it there.
level_2: The axes stay on screen but the scale suddenly zooms in or out without any smooth transition; the curve appears to be drawn in disconnected pieces rather than as one continuous line; point A shows up before the curve has finished being drawn; or the background color changes abruptly partway through the clip.
level_3: The axes stay in the same place and at the same scale for the whole clip; the curve is drawn as one continuous line from left to right; point A appears only after the curve is completely drawn, though its label may lag slightly behind the dot appearing, or the tick marks may shift very slightly as they render; the curve never crosses an axis in a way that contradicts the plotted values.
level_4: Everything required for the 3-point level is present, and in addition: the axes and their labels stay fixed in place for the entire clip; the curve's drawing motion (descending, then ascending) looks smooth rather than jumpy; point A appears with a simple, gentle animation (e.g., a brief pulse or fade-in) right at the curve's minimum, with its label staying attached to it; nothing about the axes, curve, or point A drifts to a new position once it has been drawn.
level_5: Everything required for the 4-point level is present, and in addition: the axes and gridlines never shift once drawn; the curve's downward slope and upward slope are each drawn smoothly with believable easing (starting slow and speeding up, or the reverse, rather than moving at a constant robotic rate throughout); point A's appearance is clearly timed to coincide with the curve reaching its lowest point, not noticeably before or after; and at no time does any element flicker, double up, or briefly appear in the wrong place before settling.