Consumer and Producer Surplus Worksheet with Answers

This consumer and producer surplus worksheet connects individual gains from trade to areas on a market graph. Students begin with four buyers and sellers, then solve a separate linear market and calculate the gains lost when output is restricted. It includes all data, graph instructions, and a teacher answer key. Use it after students can locate equilibrium and calculate triangle areas. The interactive graph below is for exploration; use the written data, not its default values, for the worksheet answers.

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Make it move

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

Allow about 30 minutes: seven for individual trades, ten for the graph, eight for the restriction, and five for the exit check. Students need paper, a pencil, and an optional calculator. Copy only the student section for a handout if answers should be hidden during practice.

Treat parts A and B as separate invented markets. Assume no external costs or benefits, competitive conditions, and no transaction costs. In the linear market, demand measures marginal willingness to pay and supply measures marginal cost. These assumptions matter when interpreting total surplus as gains to society in the model. This is a calculation exercise, not evidence that every real market allocation is fair.

Student worksheet

A. Find gains on individual trades

Each buyer wants at most one item, and each seller has at most one item. All completed trades occur at a price of $7. Buyers purchase when willingness to pay exceeds price; sellers sell when price exceeds their listed cost.

1. Identify the buyers and sellers who trade. How many units trade?

2. Calculate each trading buyer's consumer surplus and each trading seller's producer surplus.

3. Sum each group's surplus and then total surplus.

4. Suppose the same three units trade at $6.50 instead, with the same participants. Recalculate both groups' totals. What changes and what stays the same?

B. Move to a continuous market graph

A separate market has inverse demand P = 14 - Q and inverse supply P = 2 + Q. Price is dollars per item and quantity is items per day.

1. Solve for equilibrium price and quantity.

2. Draw price vertically and quantity horizontally. Plot both curves, label their vertical intercepts and intersection, and shade consumer and producer surplus differently.

3. Calculate both surplus triangles and their sum. Include units.

4. Calculate total revenue at equilibrium. Is it the same as producer surplus?

C. Restrict output

Now only four units per day may be traded, at a price of $8. Assume the four units go to the buyers with the highest willingness to pay and are supplied by the lowest-cost producers. Trading permissions are allocated without fees, there are no payments besides the $8 sale price, and no resources are spent obtaining permission to trade.

1. Find willingness to pay and marginal cost at Q = 4.

2. Calculate consumer surplus over the four units using a trapezoid. Repeat for producer surplus.

3. Calculate total surplus and compare it with the unrestricted outcome.

4. Show the missing gains between Q = 4 and the original equilibrium quantity as a triangle. What assumption about who trades would fail if allocation were random?

D. Exit check

A student writes, 'Producer surplus is all the money sellers receive, and a price change always changes total surplus.' Use the two markets to correct each claim.

Teacher answer key

Individual market: Ana, Ben, and Cara buy; Eli, Fran, and Gus sell. Three units trade. Buyer surpluses are $5, $3, and $1, totaling $9. Seller surpluses are $5, $3, and $1, totaling $9. Total surplus is $18. Dev and Hana do not trade and earn no surplus from a transaction.

At $6.50, the same participants still trade. Buyer surpluses become $5.50, $3.50, and $1.50, totaling $10.50. Seller surpluses become $4.50, $2.50, and $0.50, totaling $7.50. Total surplus remains $18. The price change reallocates $1.50 between groups without changing these trades.

Continuous market: Set 14 - Q = 2 + Q. Then Q = 6 and P = $8. Vertical intercepts are $14 for demand and $2 for supply; the intersection is (6, 8), using (quantity, price) coordinates. Consumer surplus is one-half x 6 x (14 - 8) = $18 per day. Producer surplus is one-half x 6 x (8 - 2) = $18 per day. Total surplus is $36 per day. Revenue is $8 x 6 = $48 per day, not producer surplus.

Restricted market: At Q = 4, willingness to pay is $10 and marginal cost is $6. Consumer surplus has vertical heights $6 at Q = 0 and $2 at Q = 4. Its trapezoid area is [(6 + 2) / 2] x 4 = $16 per day. Producer surplus has the same two heights and is also $16 per day. Total surplus is $32 per day, a loss of $4.

The lost-gains triangle has horizontal base 6 - 4 = 2 and vertical height 10 - 6 = 4, so its area is one-half x 2 x 4 = $4 per day. Random allocation could exclude higher-value buyers or include higher-cost sellers, violating the efficient-selection assumption and reducing surplus further.

Exit check: Producer surplus excludes the supply-side costs represented beneath the supply curve. Revenue does not. A price change can redistribute surplus without changing total gains when quantity and participants remain fixed, as part A demonstrates.

Follow-up and reference

Use the consumer and producer surplus guide for vocabulary and the supply and demand sandbox to discuss intersections. Its numbers are not this worksheet's key. These original exercises use surplus-area definitions checked against OpenStax, Demand, Supply, and Efficiency.