The second new species named Puntius euspilurus is an edible freshwater fish found in the Mananthavady river in Wayanad. The epithet euspilurus is a Greek word referring to the distinct black spot on the caudal fin. The slender bodied fish prefers fast flowing, shallow and clear

Question

The second new species named Puntius euspilurus is an edible freshwater fish found in the Mananthavady river in Wayanad. The epithet euspilurus is a Greek word referring to the distinct black spot on the caudal fin. The slender bodied fish prefers fast flowing, shallow and clear waters and occurs only in unpolluted areas. It appears in great numbers in paddy fields during the onset of the Southwest monsoon.

Suppose that the supply schedule of this Fish is given in the table below which follows a linear relationship between price and quantity supplied.

| Price P per kg (in ₹) | Quantity (X) of Fish Supplied (in kg) |
|---|---|
| 25 | 800 |
| 20 | 700 |
| 15 | 600 |
| 10 | 500 |
| 5 | 400 |

Suppose that this Fish can be sold only in Kerala. The Kerala demand schedule for this Fish is as follows and there is a linear relationship between price and quantity demanded.

| Price (p) per kg (in ₹) | Quantity (x) of Fish Demanded (in kg) |
|---|---|
| 25 | 200 |
| 20 | 400 |
| 15 | 600 |
| 10 | 800 |
| 5 | 1000 |

Which of the following represents the Price (p) – supply (x) relationship?
(a) $p = 65 - \frac{x}{20}$
(b) $p = 65 + \frac{x}{20}$
(c) $p = -15 + \frac{x}{20}$
(d) $p = 15 - \frac{x}{20}$

Accepted Answer

> [!TLDR]
> The supply data are linear; the slope is $	frac{1}{20}$ and, using a data point, the intercept is $-15$, giving $p=-15+	frac{x}{20}$ — option (c).

> [!FORMULA]
> **Linear relation:** $p=a+bx$, slope $b=\dfrac{\Delta p}{\Delta x}$, intercept $a$ from any point $(x,p)$.

| Price $P$ (₹) | Supply $X$ (kg) |
|---|---|
| 25 | 800 |
| 20 | 700 |
| 15 | 600 |
| 10 | 500 |
| 5 | 400 |

1. As $x$ rises by $100$, $p$ rises by $5$, so $b=\dfrac{5}{100}=\dfrac{1}{20}$ (positive — supply).
2. Model $p=a+\dfrac{x}{20}$; use $(x,p)=(800,25)$: $25=a+\dfrac{800}{20}=a+40$.
3. $a=25-40=-15$.
4. Hence $p=-15+\dfrac{x}{20}$; check $(400,5)$: $-15+	frac{400}{20}=-15+20=5$ ✓.

> [!ANSWER]
> Option **(c)** $p=-15+\dfrac{x}{20}$.

Type	What it shows	Who it's for
Individual Supply Schedule	One seller's quantities at various prices	A single firm
Market Supply Schedule	Total quantities from all sellers at various prices	The entire market

Concept understanding — Supply Schedule

Supply Schedule: From Intuition to Definition

The Precise Statement

A Concrete Example

Why This Matters

Price (₹ per glass)	Quantity Supplied (glasses per day)
5	10
10	50
15	80
20	100

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