Demand and Supply Analysis

Lessons

Senior 4 · Economics

Demand and Supply Analysis

5 lessons

Lesson 4 of 5

Supply and the law of supply

30 min

A 60% bigger coffee crop

NISR's national accounts report that in 2025 Rwanda's production of export crops rose by 32%, driven by a 60% increase in coffee production and an 8% increase in tea; food crop production rose by 3%. Farmers are sellers: how much they bring to market depends on the price they expect, but also on rain, fertiliser, the age of their trees and much else. This lesson does for sellers what the last two lessons did for buyers: it defines supply, states the law of supply, and separates a movement along the supply curve from a shift of the whole curve.

Definition

Supply: the quantity of a good that producers are willing and able to offer for sale at each possible price, over a given period, ceteris paribus.

Quantity supplied: the amount offered at one particular price.

Stock is different: it is the total amount of a good in existence, part of which may be held back from sale.

1. Types of supply

Type	Meaning	Example
Individual and market supply	One producer's supply; the total of all producers' supply at each price	One farmer's tomatoes; all tomato farmers in a district
Joint supply	Producing one good automatically produces another	Beef and hides; milk and cream
Competitive supply	Resources used for one good cannot be used for another	A hillside planted with tea or with maize
Composite supply	A good supplied from several different sources	Electricity from hydro dams, methane gas and solar panels

Definition

The law of supply: ceteris paribus, the higher the price of a good, the greater the quantity supplied, and the lower the price, the smaller the quantity supplied. Price and quantity supplied are directly (positively) related.

2. The supply schedule and the supply curve

Ten tomato farmers in a district each have the same supply schedule. Market supply is ten times one farmer's supply at each price (illustrative figures).

Point	Price (Frw per kg)	One farmer (kg per day)	Market, 10 farmers (kg per day)
v	100	20	200
w	200	60	600
x	300	100	1,000
y	400	140	1,400
z	500	180	1,800

Why the supply curve slopes upwards.

Profit motive: a higher price makes each unit more profitable, so producers offer more.
Rising costs: producing more usually raises the cost of each extra unit (Unit 6, the law of diminishing returns), so a higher price is needed to cover it.
New producers: a higher price attracts new firms and farmers into the market.
Stocks released: sellers holding stocks release more when the price rises.

Worked example 1: the supply function

One farmer's schedule fits the straight line $Q_{s} = - 20 + 0.4 P$ , and the market's $Q_{s} = 10 (- 20 + 0.4 P) = - 200 + 4 P$ .

(a) Slope of the market curve between w and x:

\frac{\Delta P}{\Delta Q} = \frac{300 - 200}{1\,000 - 600} = \frac{100}{400} = 0.25

Positive: the curve slopes upwards. Each extra 4 kg needs the price to rise by Frw 1.

(b) Quantity supplied at Frw 350: $Q_s = -200 + 4 \times 350 = 1\,200$ kg a day.

(c) The lowest price at which anything is offered: set $Q_{s} = 0$ : $0 = - 200 + 4 P$ , so $P = \text{Frw } 50$ . Below Frw 50 per kg it does not pay farmers to bring tomatoes to market at all.

3. Abnormal supply curves

Labour (backward-bending): as the wage rises, people first work more hours, but at high wages some prefer more leisure, because they can earn enough in fewer hours.
Fixed supply (vertical): the quantity cannot change whatever the price: land in a district, seats in a stadium, or fresh fish already landed today that must be sold before it spoils.
Target-income sellers (downward-sloping): a farmer who sells only to raise a fixed sum, such as school fees, sells fewer kilograms when the price is high, because fewer are needed to reach the target.
Expectations: sellers who expect prices to rise further may hold back stock now, offering less even as the price rises.

4. Determinants of supply

Determinant	Change	Effect on the supply curve
Costs of production	Fertiliser, fuel or wages become dearer	Shifts left
Technology	Better seed, irrigation, machines	Shifts right
Prices of other goods	Maize becomes more profitable than beans (competitive supply)	Supply of beans shifts left
Joint products	More cattle slaughtered for beef	Supply of hides shifts right
Number of producers	New farmers or firms enter	Shifts right
Weather and natural factors	Good rains; or drought, floods, pests	Right; or left
Government policy	Taxes on producers; subsidies; regulations	Tax: left. Subsidy: right. Strict regulation: left
Expectations	Sellers expect higher prices soon	Shifts left now (stock held back)
Time and gestation period	A coffee tree takes years to bear fruit	Supply responds slowly to price
Infrastructure and security	Better feeder roads to markets	Shifts right

Definition

Change in quantity supplied: a movement along the supply curve caused only by a change in the good's own price: an extension (more) or a contraction (less) of supply.

Change in supply: a shift of the whole supply curve caused by any other determinant: an increase (right) or a decrease (left).

Worked example 2: a subsidy and a tax shift supply (illustrative)

A fertiliser subsidy cuts one farmer's cost by Frw 50 for every kilogram. She now needs Frw 50 less per kilogram to offer the same amount, so in her supply function $P$ is replaced by $P + 50$ :

Q_{s} = - 20 + 0.4 (P + 50) = - 20 + 0.4 P + 20 = 0.4 P

At Frw 300 she now offers $0.4 \times 300 = 120$ kg instead of 100 kg. Seen vertically, the 100 kg she used to offer at Frw 300 is now offered at Frw 250: the curve has moved down by exactly the Frw 50 subsidy.

A tax of Frw 50 per kg does the reverse: $Q_{s} = - 20 + 0.4 (P - 50) = - 40 + 0.4 P$ , only 80 kg at Frw 300.

Warning

"Supply rose because the price rose" mixes two ideas. A higher price raises the quantity supplied along the curve. "Supply" rises only when the curve shifts, through lower costs, better technology, good weather or more producers. Be especially careful with farm output: was NISR's 60% rise in coffee production in 2025 a response to price, or a shift caused by the harvest itself? Coffee trees take years to mature, so most of a single year's jump in output comes from weather and the cycle of the trees, not from a price response.

Tip

Supply shifts: "costs up, curve left". Anything that makes producing dearer (taxes, dearer inputs, bad weather) shifts supply left; anything that makes it cheaper (subsidies, technology, good rains) shifts it right.

Important

Discuss. Many Rwandan farmers grow food both to eat and to sell. How might this affect the shape of their supply curve for beans? Think about a household that sells only what is left after feeding the family, and about the target-income seller.

Khan Academy, "Law of supply". Watch for the reasons a higher price leads producers to offer more, then compare them with the list in section 2.

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Practice

Distinguish between supply and stock.
Give an example of joint supply and of competitive supply, and explain each.
State the law of supply and give three reasons why the supply curve slopes upwards.
Market supply is $Q_{s} = - 200 + 4 P$ . Find the quantity supplied at Frw 250 and the price at which 1,600 kg is supplied.
Draw and explain a backward-bending supply curve of labour.
State the effect on the supply curve of maize of: (a) a fall in the price of fertiliser, (b) a rise in the price of maize, (c) drought, (d) a rise in the price of beans, grown on the same land.
A tax of Frw 30 per kg is imposed on a producer whose supply is $Q_{s} = - 60 + 2 P$ . Find the new supply function and the quantity supplied at Frw 100 before and after the tax.
"Agricultural supply responds slowly to price." Explain, with reference to coffee in Rwanda.

Show answersHide answers

Supply is the amount offered for sale at each price over a period; stock is the total amount in existence, some of which may be held back.
Joint: beef and hides (slaughtering cattle produces both). Competitive: tea and maize compete for the same land, so more of one means less of the other.
Ceteris paribus, quantity supplied rises with price. Reasons: profit motive, rising marginal costs, new producers enter (also stocks released).
$Q_s = -200 + 4 \times 250 = 800$ kg. $1\,600 = -200 + 4P$ , so $P = \frac{1\,800}{4} = \text{Frw } 450$ .
Hours worked (horizontal) rise with the wage (vertical) up to a point, then fall as workers choose more leisure once they can earn enough in fewer hours.
(a) Shifts right. (b) No shift: an extension along the curve. (c) Shifts left. (d) Shifts left: farmers switch land to beans.
$Q_{s} = - 60 + 2 (P - 30) = - 120 + 2 P$ . At Frw 100: before $- 60 + 200 = 140$ ; after $- 120 + 200 = 80$ .
A coffee tree takes years to bear fruit, so a higher price today cannot raise output today; farmers can only plant more trees, which yield years later. In the short run, output depends mainly on weather and the age of the trees, so supply is fixed or nearly fixed.

Quick check

Key points

Supply is the quantity producers are willing and able to offer at each price over a period, ceteris paribus.
The law of supply: price and quantity supplied are directly related, so the curve slopes up; a straight-line supply curve can be written $Q_{s} = c + d P$ .
Abnormal supply: backward-bending labour, fixed (vertical) supply, target-income sellers.
Own price moves along the curve; costs, technology, weather, other goods' prices, taxes and subsidies shift it.

Sources and credits

Crop production growth: GDP National Accounts, 2025, National Institute of Statistics of Rwanda (NISR).
Photo: Harvest of Irish potatoes in Rwanda West, EWRM Project, DUSABEMUNGU Ange de la Victoire, via Wikimedia Commons, CC BY-SA 4.0. Used unchanged.
Video: Law of supply, Khan Academy, embedded from YouTube.

Written by Ganzaa: the text, the supply diagrams (drawn to scale from their equations), the tables, the worked examples and the practice items. The tomato schedules, subsidy and tax figures are illustrative. The photo is shared under CC BY-SA 4.0.

1A 60% bigger coffee crop

21. Types of supply

32. The supply schedule and the supply curve

43. Abnormal supply curves

54. Determinants of supply

A 60% bigger coffee crop

1. Types of supply

2. The supply schedule and the supply curve

3. Abnormal supply curves

4. Determinants of supply