Binding and Nonbinding Price Controls Worksheet with Answers

This binding and nonbinding price controls worksheet separates three quantities students often confuse: quantity demanded, quantity supplied, and quantity actually traded. It also tests a less familiar case: a legal limit that initially has no effect but becomes binding after supply changes. Students calculate rather than role-play, making this a written follow-up to a market simulation. The interactive graph below is for exploration; use the written data, not its default values, for the worksheet answers.

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Supply and demand at equilibrium, drawn by the interactive graph. Tap it to drag the curves, open the full version, or put it on your own site free, or turn it into a five-minute class activity.

Teacher setup

Suggested duration is 25 minutes: five to find equilibrium, ten for the policy cases, five for the supply-change extension, and five to discuss the error check. Students need paper and a calculator if desired. Copy the student section without the visible answer key for independent work.

The invented market sells notebooks. Quantities are notebooks per day and prices are dollars per notebook. Assume competitive buyers and sellers, no government purchases, no illegal trades, and no changes in product quality. When a control binds, assume trades take place at the legal limit and all possible trades between willing buyers and sellers are completed. Quantity traded therefore equals the smaller of quantity demanded and quantity supplied.

Student worksheet

A. Establish the comparison price

Demand is Qd = 140 - 10P. Supply is Qs = 20 + 10P.

1. Solve for the unregulated equilibrium price and quantity.

2. Define a price ceiling and a price floor. Does either definition require the actual price to equal the legal limit?

3. Sketch both curves. Label the equilibrium and draw horizontal lines at $4, $7, and $8.

B. Evaluate independent policies

Each policy starts from the original market. Complete a table with these columns: binding or nonbinding; predicted actual price; quantity demanded at that price; quantity supplied at that price; shortage or surplus; quantity traded.

For each nonbinding policy, explain why substituting the legal limit into both equations does not identify the predicted market outcome. For each binding policy, calculate the imbalance and explain why it differs from the number of completed sales.

C. When a previously harmless limit matters

Replace the four independent policies with a single maximum price of $7. Is it initially binding? Now production costs rise and supply becomes Qs = -20 + 10P for P at least $2; below $2, quantity supplied is zero. Demand does not change.

1. Calculate the new equilibrium if the government removes the ceiling.

2. Keep the $7 ceiling. Calculate quantity demanded, quantity supplied, the shortage, and quantity traded.

3. Sketch the new supply curve and explain why a law that initially did not constrain the market now does.

D. Catch the error

A classmate writes, 'A price floor of $8 means producers sell 100 notebooks. A ceiling of $8 makes buyers purchase only 60.' Identify what is wrong with both claims.

Teacher answer key

Original equilibrium: 140 - 10P = 20 + 10P gives 120 = 20P, so P = $6 and Q = 80 notebooks per day. A ceiling sets a maximum legal price; a floor sets a minimum. Neither forces a nonbinding limit to become the actual market price.

The nonbinding ceiling allows the equilibrium price of $6 because $6 is below $8. The nonbinding floor also allows $6 because $6 is above $4. Substituting those legal limits instead would answer a hypothetical question about quantities at an imposed price, not the actual outcome of a maximum or minimum that leaves equilibrium feasible.

The binding ceiling's shortage is 100 - 60 = 40, while 60 notebooks trade. The binding floor's surplus is 100 - 60 = 40, while buyers purchase 60. A quantity offered is not a guarantee that every offered item sells.

Extension: The $7 ceiling initially does not bind because equilibrium is $6. After the supply decrease, 140 - 10P = -20 + 10P gives P = $8 and Q = 60 without the control. At the binding $7 ceiling, Qd = 70 and Qs = 50. The shortage is 20 notebooks per day and 50 trade under the stated matching assumption. On the graph, the new uncontrolled crossing is (60, 8), above the ceiling; quantities at the ceiling are 50 supplied and 70 demanded.

Error check: Under the $8 floor, producers offer 100 but sell only 60 to private buyers in this model. Under the $8 ceiling, the price remains $6 and 80 trade. Both mistakes treat a different number as completed sales.

Follow-up

Have students first circle whether the unconstrained equilibrium is legal. Only then calculate a controlled-price imbalance. The shortage and surplus worksheet supplies prerequisite practice. The price-controls classroom activity offers a separate trading simulation.

Concept reference

The notebook model and answer key are original. Legal maxima, minima, and controlled-price imbalances are checked against OpenStax, Price Ceilings and Price Floors.