Q.A monopolist selling in two separate markets, A and B, has a constant Marginal Cost of Rs. 10. The demand functions are PA=50−QA in Market A and PB=40−2QB in Market B. Find the profit-maximising price and quantity in each market, verify that MRA=MRB=MC, and calculate total profit.
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🔒 Start your 14-day free trial to unlock the full solution →Concept understanding — Price Discrimination
Price discrimination occurs when a seller (typically a monopolist) charges different prices to different buyers for the same product, and the price gap is not justified by any difference in cost. The aim is to capture more consumer surplus as profit.
Same product, different prices, same cost — that is discrimination. It only works if the seller can keep the markets apart and those markets differ in how price-sensitive they are.
How it works
The firm splits buyers into groups and charges each group what it is willing to pay. In third-degree discrimination it allocates output so that marginal revenue is equal across markets (MRA=MRB). Using MR=P(1−∣e∣1), equal MR forces the less elastic market to carry the higher price.
Three conditions must ALL hold for price discrimination:
- The seller has market power (a monopoly or strong pricing control).
- Markets can be separated — no resale/arbitrage between them.
- The markets have different price elasticities of demand.
Quick example
A monopolist serves two separable markets. At the profit-maximising output it sets a common marginal revenue of MR = ₹30. Market A has elasticity eA=2; Market B has eB=4. Find each price.
- Rearrange the formula: P=1−e1MR.
- Market A: PA=1−2130=0.530=₹60.
- Market B: PB=1−4130=0.7530=₹40.
| Market | Elasticity e | Price P |
|---|---|---|
| A (less elastic) | 2 | ₹60 |
Find MR in each market separately, set each equal to the common MC to find each market's quantity and price, then verify the two MR values are equal and sum the profits.
Market A: Q=20, P=Rs.30. Market B: Q=7.5, P=Rs.25. Both MR=Rs.10=MC. Total profit=Rs.512.5.
Market A: TRA=50QA−QA2, MRA=50−2QA. Set =10: QA=20, PA=30.
Market B: TRB=40QB−2QB2, MRB=40−4QB. Set =10: QB=7.5, PB=25. …
Market A: TRA=PA×QA=(50−QA)QA=50QA−QA2, so MRA=50−2QA. Setting MRA=MC=10:
50−2QA=10⇒QA=20,PA=50−20=Rs.30
Market B: TRB=PB×QB=(40−2QB)QB=40QB−2QB2, so MRB=40−4QB. Setting MRB=MC=10:
40−4QB=10⇒QB=7.5,PB=40−2(7.5)=Rs.25
Verification of the price-discrimination rule: MRA=50−2(20)=10 and MRB=40−4(7.5)=10 — both equal Rs. 10, which is also equal to MC, exactly satisfying MRA=MRB=MC.
Total profit:
Profit=(PA−MC)QA+(PB−MC)QB=(30−10)(20)+(25−10)(7.5)=400+112.5=Rs.512.5 …
As a cross-check, if the same 27.5 total units were instead sold as a single undiscriminated batch split evenly and arbitrarily (say Q_A=15, Q_B=12.5) instead of at the MR-equalising split, the two markets' marginal revenues would NOT be equal (MR_A at Q_A=15 is 50-30=20, MR_B at Q_B=12.5 is 40-50=-10) — since MR_A > MR_B here, shifting units from B to A …
A common mistake is charging the SAME price in both markets (treating them as one combined market) — this fails to exploit the different elasticities of demand and yield …
- CA Foundation 2026Set jan-20261 markMCQQ.Consider a monopolist selling in two markets. At a price of 60, the elasticity of demand in market A is 5 and in market B is 6. Calculate the marginal revenue in both markets and determine which market should receive more output. (A) Market A, MR = 48; Market B, MR = 50, output to market B should increase (B) Market A, MR = 50; Market B, MR = 48, output to market A should increase (C) Both markets have equal MR (D) Neither market should change output
›Reveal solutionSolution
With P=60: MRA=60(1−1/5)=48 and MRB=60(1−1/6)=50; since MRB>MRA, sell more in market B.
Working — price discrimination across markets
Formula, with P=60:
MR=P(1−E1)
Market A (E=5):
MRA=60(1−51)=60×0.8=48
Market B (E=6):
MRB=60(1−61)=60×65=50
A profit-maximising monopolist equalises MR across markets by reallocating output to where MR is higher. Here MRB(50)>MRA(48), so output should be increased in market B (the more elastic market, which also gets the lower price). …
- CA Foundation 2025Set may-20251 markMCQQ.Which of the following is not a condition for price discrimination ? (A) The seller should have price setting power. (B) The seller should be able to divide his market into two or more sub markets. (C) The price elasticity of the product should be different in different sub markets. (D) It should be possible for buyers of low-priced market to resell the product to the buyers of high-priced market.
›Reveal solutionSolution
A necessary condition is that resale between sub-markets is IMPOSSIBLE; (D) states the opposite, so it is not a condition.
Step 1 — Conditions required for price discrimination
- The seller must have price-setting (monopoly) power.
- The market must be divisible into two or more separable sub-markets.
- The elasticity of demand must differ across the sub-markets (so different prices are profitable).
- No resale (no seepage) — buyers in the cheap market must NOT be able to resell to the dear market, otherwise arbitrage wipes out the price gap.
Step 2 — Match the options
- (A) price-setting power — a valid condition.
- (B) ability to divide the market — a valid condition.
- (C) different elasticities in sub-markets — a valid condition.
- (D) buyers of the low-priced market CAN resell to the high-priced market — this is the very thing price discrimination must PREVENT. Stated as a condition, it is false. …
- CA Foundation 2025Set sep-20251 markMCQQ.Which one of the following is not the object of price discrimination ? (A) To earn maximum profit (B) To enjoy economies of scale (C) To hold excess stock (D) To secure equity through pricing
›Reveal solutionSolution
Holding excess stock is not an aim of price discrimination — it disposes of surplus, so option (C) is the odd one out.
Step 1 — List the genuine objectives
A discriminating monopolist practises price discrimination to:
- Earn maximum profit by charging each segment what it will bear.
- Enjoy economies of scale by selling larger output at differentiated prices.
- Secure equity — charge the rich more and the poor less (e.g. utility/rail tariffs), a welfare objective.
Step 2 — Test the odd option
Holding excess stock is not a purpose. Price discrimination is used to sell off surplus in a separate market, not to retain it. So it is the item that is NOT an object.
Step 3 — Select …
- CA Foundation 2024Set sep-20241 markMCQQ.A software company engages in price discrimination for its product. The company identifies different market segments and charges different prices based on perceived differences in willingness to pay. This is possible under which situation ? (A) Monopolistic competition (B) A Monopoly (C) Perfect competition (D) Oligopoly competition
›Reveal solutionSolution
Price discrimination requires price-setting power and separable markets — conditions met under monopoly.
Step 1 — Conditions for price discrimination
To charge different prices for the same good the seller must (i) be a price MAKER with market power, (ii) be able to divide buyers into separable segments with different willingness to pay, and (iii) prevent resale between segments.
Step 2 — Which structure fits
A monopoly is a single seller with genuine control over price, able to segment its market and stop arbitrage — so it can practise price discrimination. Under perfect competition (C) firms are price takers and cannot; monopolistic competition (A) and oligopoly (D) have market power but the pure, textbook setting for price discrimination is monopoly. …
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