Demand, supply and changing prices

Imagine a weekly market for boxes of identical notebooks. Buyers have different uses for notebooks, and sellers face different costs and capacities. Rather than describe every person separately, we summarise their plans at each possible price. The model asks what quantity would be demanded and supplied if that price prevailed while specified other conditions remained unchanged. It does not assume that every quoted price is actually observed or that all planned trades occur. Define the product, quality, location, period and units before combining different people’s plans into market schedules.

Read the equation as a conditional plan. Substitute 10 for P: 60 minus twice 10 equals 40 boxes per week. Substitute 15: 60 minus 30 equals 30. The negative coefficient represents a downward-sloping demand relationship over the relevant range. It does not mean people always buy fewer boxes whenever a higher price is observed in the real world; other conditions might have changed too. This linear schedule is intended only for prices that imply meaningful non-negative quantities. Extending it indefinitely to predict negative purchases would misuse the model.

Suppose the notebook price falls while incomes, preferences and other relevant circumstances stay fixed. The original schedule tells us the new quantity demanded: that is a movement along it. Now suppose a new group of students enters the market. More boxes might be wanted at every notebook price, requiring a different schedule. That is a shift. Income effects depend on the good: demand for a normal good rises with income, while demand for an inferior good can fall. These labels describe responses to income, not a moral or physical judgement about the product’s quality.

Substitute the price into the supply equation just as we did for demand. Twelve plus ten gives twenty-two boxes; twelve plus fifteen gives twenty-seven. The positive relationship can reflect additional production becoming worthwhile as price covers higher marginal costs. It may also involve inventories or entry over the relevant time horizon. A market supply schedule need not be upward sloping in every possible setting. Our simple model assumes a competitive setting in which individual sellers take price as given and can adjust quantity. Later models can examine market power, fixed capacity and strategic pricing.

Suppose the price of paper falls while notebook prices remain unchanged. Producing boxes may become worthwhile for sellers who previously found it too costly. This is an outward supply shift. By contrast, a rise in the notebook price with unchanged production conditions moves sellers along the existing schedule. Be precise about the time horizon. Tomorrow’s supply may depend on stock already printed, whereas next year’s supply can include new equipment and firms. The same event may therefore have different short-run and long-run effects. A useful prediction specifies which adjustment opportunities are available.

Step one writes the equilibrium condition: quantity demanded equals quantity supplied. Step two collects the constant terms on one side and price terms on the other. Starting with 60 minus 2P equals 12 plus P, subtracting 12 gives 48 minus 2P equals P. Adding 2P gives 48 equals 3P. Step three divides both sides by three to obtain 16 pounds per box. Step four substitutes this price into both original equations. Both give 28 boxes per week, so the calculation is internally consistent. Equality is a model condition, not a guarantee that any actual price instantly adjusts to it.

First evaluate both schedules at the same price and over the same period. Second subtract supplied quantity from demanded quantity: 36 minus 24 equals 12. That difference measures unmatched purchase plans, not necessarily a recorded queue of exactly twelve boxes. Actual sales may be limited by available supply and by matching or other frictions. Buyers might compete through higher offers, waiting or search effort. Which adjustment occurs depends on the market’s rules. Scarcity remains at the equilibrium too, because producing and buying notebooks still uses resources that have alternative uses even when no excess demand appears in this model.

Calculate demand as 60 minus twice 20, which gives 20. Calculate supply as 12 plus 20, which gives 32. Subtract demand from supply: 32 minus 20 equals 12. Some sellers may cut prices, reduce output, store goods or seek other buyers. Our static model does not specify the speed or exact process of adjustment. Nor does a planned surplus prove that twelve physical boxes have already been produced and wasted. Supply is a planned quantity at a price; the timing of production and whether unsold inventories exist require additional information.

Step one identifies what changed: the demand intercept rises from 60 to 72, while its price coefficient and the entire supply schedule remain unchanged. Step two equates the new demand with the old supply. Rearranging gives 60 equals 3P, so price is 20. Step three substitutes: 12 plus 20 gives 32 boxes. Compared with the original equilibrium, price rises by four pounds and quantity by four boxes. Quantity demanded also changes, but calling this only a movement along demand misses the initial change in conditions. The equilibrium comparison uses two different demand curves.

Begin from the original baseline rather than silently carrying forward the previous demand shift. The new equality rearranges to 54 equals 3P, which gives a price of 18. At that price, demand is 60 minus 36, or 24 boxes. Supply is 6 plus 18, also 24. Relative to the original price of 16 and quantity of 28, price increases by two pounds and quantity falls by four boxes. The higher price partly offsets the supply contraction through movements along the schedules. It does not undo the underlying loss of supply at each given price.

Combine the two shifted schedules and solve rather than adding verbal predictions mechanically. Seventy-two minus 2P equals six plus P becomes 66 equals 3P, so price is 22. Supply then gives six plus 22, or 28 boxes. Demand gives the same result. In this particular numerical case, the quantity effects exactly offset. Other shift sizes could raise or lower quantity. A qualitative diagram often identifies some directions but leaves others ambiguous. Saying that an effect is ambiguous without additional information is a valid analytical conclusion, not a failure to understand the model.

Two observed transactions cannot reveal an entire demand curve if demand or supply shifted between them. For example, a festival could increase both the number of buyers and sellers’ staffing costs. Observed price and quantity would reflect both mechanisms. To investigate causality, look for evidence about the changes in relevant conditions, a credible comparison group, or a research design that separates influences. Even then, report uncertainty. The phrase “holding other things constant” is a condition of a model comparison; it is not something we can assume simply because a spreadsheet records only price and quantity.

A price can clear a market even when some people cannot afford the product, when ownership is disputed, or when production imposes pollution costs on neighbours. Those issues are not disproved by the intersection of two curves. Under particular competitive assumptions, economists can make stronger claims about gains from trade and allocation, but the assumptions must be stated. A liberty-oriented perspective may prioritise voluntary exchange and secure rights; another perspective may weigh distribution differently. Clear analysis separates the mechanism that determines an outcome from the ethical reasons for supporting, changing or rejecting the institutions around it.

A diagram and an equation can tell the same story if they use consistent axes and definitions. Conventionally, price appears on the vertical axis and quantity on the horizontal axis, even though our equations express quantity as a function of price. You can practise without a graph by checking quantities at several prices. The exercises use new schedules and require explicit numerical answers. Reflection fields are ungraded: they are a place to explain which conditions must remain fixed or why observed correlations are insufficient. Avoid converting a correct algebraic solution into an unsupported claim about a real market.