📐 The Linear Supply Function
Standard form: The linear supply function is written as: $$Qs = c + dP$$ where c = quantity supplied when price is zero (the Q-intercept) and d = the responsiveness of quantity supplied to a change in price.
- c can be positive, zero, or negative. If c < 0, there is a minimum price before any supply occurs.
- d is the slope parameter — it tells you how many additional units are supplied for each $1 increase in price.
- P is the price of the good.
- The positive sign reflects the direct relationship: as P rises, Qs rises (law of supply).
Finding the P-intercept
The P-intercept (minimum supply price) is found by setting : $$0 = c + dP \implies P = -\frac{c}{d}$$ If c is negative, the P-intercept is positive — firms need a minimum price before they are willing to supply.
Worked example: If , then: c = −20, d = 4. P-intercept = −(−20)/4 = $5. No supply below $5. At P = $10: Qs = −20 + 40 = 20 units.
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📈 Graphing and Shifts of the Linear Supply Curve
- On the economics diagram (P vertical, Q horizontal), the supply curve has slope .
- A change in P → movement along the supply curve.
- A change in c → parallel shift of the supply curve.
- Increase in c → supply shifts RIGHT (more supplied at every price).
- Decrease in c → supply shifts LEFT (e.g. higher input costs).
- A change in d changes the SLOPE (steepness).
Factors that shift supply (input costs, technology, number of firms, government policies) change the value of c. If input costs rise, c falls → curve shifts left (less supplied at each price).