Price elasticity and the cobweb model of farm prices
Why farm prices swing so much: price and income elasticity of food demand, the paradox of a good harvest, and the cobweb model of boom-and-bust cycles.
On this page
Farm prices are more volatile than the prices of almost anything else people buy. A good season can leave farmers poorer than a bad one; a year of high onion or pork prices is often followed by a glut. Two ideas explain most of this: elasticity, which measures how strongly buyers and sellers respond to price, and the cobweb model, which shows what happens when producers decide what to grow before they know the price they will get.
Both are standard in agricultural economics and marketing courses, and both come with calculations.
Price elasticity of demand
The price elasticity of demand measures how much the quantity demanded responds to a change in price:
It is negative, because people buy less when price rises; it is usually quoted as a number without the sign, or the sign is kept and "more negative" means "more elastic".
| Value of Ed (absolute) | Description | What happens to total spending when price rises |
|---|---|---|
| greater than 1 | elastic | falls |
| equal to 1 | unit elastic | unchanged |
| less than 1 | inelastic | rises |
| 0 | perfectly inelastic | rises in proportion to price |
For a calculation between two points, the arc (midpoint) formula avoids getting a different answer depending on the direction of change:
Why food demand is inelastic
The demand for staple foods as a whole is inelastic: estimates for cereals and other staples are commonly around −0.1 to −0.5. People cannot eat much more rice or bread because it is cheaper, and they do not stop eating because it is dearer. Demand for a single product with close substitutes (one variety of apple, one brand) is more elastic; demand for food in total is the least elastic.
Two related measures matter too:
- Income elasticity of demand: the response to income. For staple foods it is low and falls as people grow richer (Engel's law: the share of income spent on food declines as income rises), while for meat, dairy, fruit and vegetables it is higher. This shifts what farmers are asked to produce as economies grow.
- Cross-price elasticity: the response of one good's demand to another's price; positive for substitutes (wheat and rice in many diets), negative for complements.
The paradox of a good harvest
Combine inelastic demand with a supply that the weather can shift suddenly, and prices swing widely. With demand inelastic, a large harvest can lower total revenue.
How a bumper crop can reduce farm income
The price elasticity of demand for a crop is −0.25. Good weather raises the harvest by 10 per cent. How much must the price fall to sell it, and what happens to total revenue?
- Required price change = % change in quantity ⁄ elasticity = 10 ⁄ (−0.25) = −40 per cent.
- Revenue = price × quantity: (1 − 0.40) × (1 + 0.10) = 0.60 × 1.10 = 0.66.
Total revenue falls by about 34 per cent, even though farmers produced more. (The constant-elasticity calculation is approximate for a change this large, but the direction is the point.)
This observation is old: it is often called King's law, after the seventeenth-century English statistician Gregory King, who noted that small shortfalls in the grain harvest raised prices far more than proportionally.
For an individual farmer, whose output is too small to move the market price, a bigger harvest is still good. It is the industry as a whole that loses when everyone has a good year. This tension, between what is rational for one farmer and what happens to all of them together, is at the root of many farm policies.
Price elasticity of supply
Supply elasticity measures how much producers change output in response to price. For most crops it is low in the short run: once a crop is planted, output depends on the weather, not the price. It is higher in the long run, as farmers change what and how much they plant, adopt new technology or invest. Perennial crops such as coffee, cocoa, rubber and fruit trees have very long lags, taking years to come into bearing.
The cobweb model
The cobweb model, named by Nicholas Kaldor in 1934 and set out as the cobweb theorem by Mordecai Ezekiel in 1938, explains regular boom-and-bust cycles in some farm markets: pigs (the "hog cycle"), potatoes, onions and other vegetables.
Assumptions
- A production lag: output must be decided a season or more before it is sold.
- Naive expectations: producers plan this season's output on last season's price.
- Price is set by the current supply: the whole harvest must be sold in the period, so price is whatever clears it, read off the demand curve. Perishability or lack of storage make this realistic.
How the cycle runs
- A high price this season encourages farmers to plant a large area.
- Next season, the big harvest can be sold only at a low price.
- The low price discourages planting, so the following harvest is small and the price high again.
Traced on a supply-and-demand diagram, the path of prices and quantities looks like a spider's web.
Three outcomes
| Case | Condition | Result |
|---|---|---|
| Convergent (damped) | supply less price-elastic than demand: supply curve steeper than demand | swings shrink, approaching equilibrium |
| Divergent (explosive) | supply more price-elastic than demand: supply curve flatter than demand | swings grow larger each cycle |
| Continuous (stable oscillation) | elasticities equal | the same cycle repeats indefinitely |
In real markets, divergent cycles do not explode for ever: storage, trade, and producers learning from experience all damp them.
Criticisms and refinements
The weakest assumption is naive expectations. Farmers who see the cycle can plan against it; later models replaced naive expectations with adaptive expectations (a weighted average of past prices) and rational expectations (forecasts using all available information), which damp or remove the cycle. Even so, cycles remain visible in markets with long production lags and little storage, and the cobweb model remains the standard teaching example.
What reduces the swings
- Storage and warehouse receipt systems, which spread a glut over time.
- Trade, which spreads a local glut or shortage over a larger market.
- Forward contracts, contract farming and futures markets, which let a farmer know a price before planting.
- Market information and outlook services: published planting intentions and price forecasts help farmers avoid all moving the same way.
- Price stabilisation policies: support prices, public procurement, buffer stocks and variable import levies, each with its own costs.
- Diversification of crops and processing outlets.
Key points
- Ed = % change in quantity ⁄ % change in price; below 1 (in absolute value) is inelastic.
- Demand for staple food is inelastic (often −0.1 to −0.5), so supply shocks cause large price changes.
- With inelastic demand, a bumper harvest can lower total farm revenue (King's law).
- Engel's law: the share of income spent on food falls as income rises.
- Cobweb model: production lag + naive expectations + price set by current supply → boom-and-bust cycles.
- Convergent if supply is less elastic than demand, divergent if more, continuous if equal; storage, trade, contracts and information damp the cycle.
What the exams ask
- School-leaving and entrance papers: definitions of elasticity and its types, and examples of elastic and inelastic goods.
- Degree and research-fellowship entrances: arc elasticity calculations, the effect of elasticity on revenue, King's law, Engel's law, the cobweb assumptions and the conditions for convergence and divergence.
- Civil-service and professional examinations: price stabilisation policy, buffer stocks, futures markets and market information as responses to farm price instability.
Described in general terms: the kind of examination, not a past paper. Laisha never reproduces exam questions.
Questions people ask
Is a good harvest bad for farmers?
For the farm sector as a whole, a very large harvest can reduce total income because prices fall more than output rises. For one farmer whose harvest is good when others' are not, it is clearly good. Storage, trade and contracts reduce the problem.
Why are pig and vegetable prices particularly cyclical?
They have production lags of months to a year, limited storage, and many producers who respond to recent prices, exactly the conditions of the cobweb model.
Why does elasticity matter for taxes and subsidies?
Elasticities decide who bears a tax or receives a subsidy: the less elastic side of the market bears more of a tax and captures more of a subsidy. They also determine how much a policy changes production and consumption.
Sources
- Ezekiel, M. "The cobweb theorem." Quarterly Journal of Economics 52, 255–280 (1938).
- Kaldor, N. "A classificatory note on the determinateness of equilibrium." Review of Economic Studies 1, 122–136 (1934).
- Tomek, W. G. and Kaiser, H. M. Agricultural Product Prices, 5th edition. Cornell University Press, 2014.
- Kohls, R. L. and Uhl, J. N. Marketing of Agricultural Products, 9th edition. Prentice Hall, 2002.
- FAO. The State of Agricultural Commodity Markets. Food and Agriculture Organization of the United Nations, recent editions.
More in agricultural economics and marketing
Discussion
Questions, corrections and notes from readers on this article. Every comment is checked before it appears: keep it on the topic, and do not share phone numbers, links or contact details.