Student Discount at Zenith Academy: Price Discrimination Under Two Elasticities
Zenith Academy sells a recorded online course for a professional certification at a flat fee of ₹6,000. Last year it enrolled 1,000 learners - about 650 students and 350 working professionals - and it treats these as two distinct markets. Variable cost per enrolment (mentoring, assessment, server load) is ₹1,500; course development, marketing and platform costs are fixed at ₹32 lakh a year. A new marketing manager proposes a 20% 'student' discount (fee ₹4,800) to lift student numbers, pointing out that competitors charge students less. Zenith's own research suggests a price elasticity of about −2.5 for students and −0.8 for professionals in the current price range. Access is through a login code; the course content is identical for both groups, and a code, once activated, is tied to one account. The manager also wants to raise the professional fee by 10% at the same time.
1. Assuming the elasticities hold, compute the effect of the 20% student discount alone on enrolment, revenue, contribution and profit. Should Zenith offer it?
Read the worked answer
Student segment. % change in numbers = (−2.5) × (−20%) = +50% → 650 × 1.5 = 975 students
| Item | Before | After |
|---|---|---|
| Student revenue | 650 × 6,000 = ₹39,00,000 | 975 × 4,800 = ₹46,80,000 |
| Professional revenue | 350 × 6,000 = ₹21,00,000 | unchanged ₹21,00,000 |
| Total revenue | ₹60,00,000 | ₹67,80,000 |
| Contribution per student | ₹4,500 | ₹3,300 |
| Student contribution | ₹29,25,000 | ₹32,17,500 |
| Professional contribution | ₹15,75,000 | ₹15,75,000 |
| Total contribution | ₹45,00,000 | ₹47,92,500 |
| Profit after ₹32,00,000 fixed | ₹13,00,000 | ₹15,92,500 |
Reasoning. Unlike a price cut on a thin-margin product, this discount works because the margin is fat: a 20% cut takes only ₹1,200 off a ₹4,500 contribution. The volume needed merely to hold student contribution is 29,25,000 ÷ 3,300 = 886 students, a rise of 36.4%; the assumed +50% clears that bar comfortably.
Decision: offer the discount, provided student status can be verified cheaply. The gain of about ₹2.93 lakh in contribution is conditional on the elasticity being right; if the true student elasticity were only −1.4, volume would rise 28% to 832 and student contribution would fall, so the scheme should be piloted and measured before it is advertised permanently.
2. Evaluate the proposed simultaneous 10% increase in the professional fee. What does the contrast between −2.5 and −0.8 imply about where Zenith's pricing power lies?
Read the worked answer
Professional segment at ₹6,600. % change in numbers = (−0.8) × (+10%) = −8% → 350 × 0.92 = 322 learners Contribution per learner = 6,600 − 1,500 = ₹5,100 → 322 × 5,100 = ₹16,42,200, against ₹15,75,000 before, a gain of ₹67,200.
Combined with the student discount: total contribution = 32,17,500 + 16,42,200 = ₹48,59,700; profit = 48,59,700 − 32,00,000 = ₹16,59,700 (up from ₹13,00,000).
Interpretation of the two elasticities. Professionals are inelastic (|e| < 1): they are buying a credential tied to career outcomes and are less responsive to price, so a rise in price raises revenue and contribution. Students are elastic (|e| > 1): a cut raises their revenue but only pays because the unit margin is large. The general rule is that the segment with the lower elasticity should carry the higher price - the manager's instinct to discount 'because competitors do' would be exactly wrong if applied to the professional group.
Caution. With |e| < 1 near unity in absolute terms, the estimate is fragile; a 10% rise is close to the range where professionals might defer or choose a rival certification. Test the rise on new cohorts rather than on renewals, and watch the conversion rate for two intakes before extending it.
3. What conditions must hold for this two-price structure to work in practice, and what could break it?
Read the worked answer
Conditions for workable price discrimination.
- Market separation with different elasticities - confirmed by the −2.5 and −0.8 estimates; without a real difference the lower price simply cannibalises the higher one.
- No resale or arbitrage - here a login code binds to one account, which blocks the classic leak. If a student could buy and hand over access, the professional price would collapse.
- Cheap, verifiable eligibility - student identity must be checkable at enrolment without a costly manual process; otherwise the administration cost eats the ₹67,000–₹2,90,000 of extra contribution computed.
- Legal and reputational comfort - differential pricing on a verifiable status is normal, but a public backlash is possible if the professional fee rise is not matched by visible value, such as live sessions or placement support.
What would break it. A professional who enrols on a student code (self-selection leakage) is the main risk: the firm would lose ₹1,800 per converted learner. Code sharing across accounts after activation, employer-sponsored bulk buying that demands the student rate, and competitor pricing that undercuts the ₹6,600 fee are the others. Finally, the elasticities are short-run point estimates; a 20% discount and a 10% increase are both large moves, so arc elasticities and live conversion data should replace the research numbers at the first review.