Midpoint Elasticity Worksheet with Worked Answers

Use this midpoint elasticity worksheet to check whether students can choose the correct percentage bases, interpret a coefficient, and separate elasticity from slope. Three invented price-quantity pairs yield elastic, inelastic, and unit-elastic results. A reverse-direction calculation exposes why using starting values can give inconsistent answers. The full teacher key follows the student tasks. The interactive graph below is for exploration; use the written data, not its default values, for the worksheet answers.

Teacher setup

Suggested time is 25 minutes: five to review the formula, ten for the three cases, five for reversing direction, and five for the exit explanation. Students need a calculator and paper. Copy the student section into a handout or LMS; the answers remain visible on this page.

Each row describes movement along one unchanged demand curve for a separate hypothetical product. Quantities are items per week, and prices are dollars per item. Do not interpret the rows as actual business evidence or compare quantities across products. Hold tastes, income, and all other demand influences constant. This worksheet measures elasticity over an interval, not a coefficient guaranteed to apply at every possible price.

Student worksheet

A. Write the calculation before entering numbers

Use these formulas, with averages taken from the two endpoints:

Percentage change in Q = [(Q2 - Q1) / ((Q1 + Q2) / 2)] x 100.

Percentage change in P = [(P2 - P1) / ((P1 + P2) / 2)] x 100.

Price elasticity of demand = absolute value of (percentage change in Q / percentage change in P).

For each case, show the quantity average, price average, both signed percentage changes, elasticity magnitude, and classification. Keep full calculator precision until the final answer, then round elasticity to two decimal places.

Classify magnitudes above one as elastic, below one as inelastic, and equal to one as unit elastic.

B. Reverse the trip

Recalculate case C going from price $5 and quantity 70 back to price $6 and quantity 50. Which signs change? Which averages and final magnitude stay the same? Then calculate case C in its original direction using the starting quantity and starting price instead of the averages. Why should that answer not be labeled a midpoint result?

C. Check total revenue

For all three cases, calculate original and new total revenue as price multiplied by quantity. State whether revenue rises, falls, or stays the same. Do your results agree with the elasticity classification over each interval? Does higher revenue prove higher profit? Explain what information would be missing.

D. Exit check

A student says, 'The elasticity in case C is -20 because quantity changed by 20 and price changed by -1. Demand must be inelastic because the result is negative.' Correct the calculation method and both interpretations.

Teacher answer key

Case A: Average Q is 50 and average P is $10. Quantity changes by 20 / 50 x 100 = 40%. Price changes by -4 / 10 x 100 = -40%. Elasticity magnitude is 1.00, so the interval is unit elastic. Revenue is $12 x 40 = $480 initially and $8 x 60 = $480 afterward. It is unchanged.

Case B: Average Q is 95 and average P is $11. Quantity changes by -10 / 95 x 100 = approximately -10.5263%. Price changes by 2 / 11 x 100 = approximately 18.1818%. Their absolute ratio is 11 / 19, or approximately 0.58, so demand is inelastic over the interval. Revenue rises from $10 x 100 = $1,000 to $12 x 90 = $1,080, an $80 increase.

Case C: Average Q is 60 and average P is $5.50. Quantity changes by 20 / 60 x 100 = approximately 33.3333%. Price changes by -1 / 5.5 x 100 = approximately -18.1818%. Elasticity magnitude is 11 / 6, or approximately 1.83, so demand is elastic over the interval. Revenue rises from $6 x 50 = $300 to $5 x 70 = $350, a $50 increase.

Reverse check: The averages remain 60 and $5.50. Quantity change becomes approximately -33.3333% and price change approximately 18.1818%. The magnitude remains 1.83. Using starting values in the original direction gives 40% divided by approximately -16.6667%, with magnitude 2.40. That calculation uses different bases, not the specified midpoint method.

The revenue results fit the respective interval classifications. Higher revenue does not establish higher profit because cost changes are not supplied. The exit calculation uses raw unit changes rather than percentage changes. A negative signed demand elasticity indicates opposite price and quantity movements here; classification uses the coefficient's magnitude, not its sign.

Follow-up

For students mixing denominators, require two boxes labeled average price and average quantity before any division. Extend with the total revenue test guide. For a whole-class extension, use the elasticity lesson plan to connect calculations with demand determinants and a pricing decision.

Concept reference

The numerical cases and questions are original. Formula, classification, and reverse-direction consistency are checked against OpenStax, Price Elasticity of Demand and Price Elasticity of Supply.