Indian Economic Service

Welcome to Indian Economic Service. We will study Consumer Theory: Utility Maximisation and the Slutsky Equation, work through an example, and practise using the course's learning material. Academic and examination-focused preparation for economics aspirants seeking central service opportunities. Sign in and use the study header to open your authorised course. Select this published lesson. Start Course Tutor with Auto audio on: it teaches continuously, answers a typed question, then resumes. A price change has two effects. The substitution effect is the change in quantity when relative prices change but real income is held constant. It is always non-positive for own price, because a consumer on a convex indifference curve always moves away from the good that has become relatively dearer. Problem. A consumer has U = x^0.5 y^0.5, income M = 100, Px = 2 and Py = 5. The price of x rises to 4. Find the substitution and income effects using the Slutsky method. Step 1: original demand. With equal exponents, half of income goes on each good. x0 = 0.5 times 100 / 2 = 25. y0 = 0.5 times 100 / 5 = 10. Check: 2 times 25 + 5 times 10 = 50 + 50 = 100. Step 2: new demand at Px = 4. x1 = 0.5 times 100 / 4 = 12.5. Total effect = 12.5 − 25 = −12.5. Step 3: compensated income. The original bundle (25, 10) costs 4 times 25 + 5 times 10 = 100 + 50 = 150 at new prices. So M′ = 150. Step 4: compensated demand. x′ = 0.5 times 150 / 4 = 75/4 = 18.75. Step 5: decompose. Substitution effect = 18.75 − 25 = −6.25. Income effect = 12.5 − 18.75 = −6.25. Sum = −12.5, which matches the total effect. Second check. Recompute: 0.5 times 150 = 75; 75 divided by 4 = 18.75. Original 25 minus 18.75 is 6.25. 18.75 minus 12.5 is 6.25. The two effects are equal here because with Cobb-Douglas utility the good is normal and the income elasticity is one. Both effects are negative, so x is a normal good. Interpretation. Half of the fall in demand comes from x becoming relatively dearer and half from the consumer being poorer. If an examiner changes the function to one where the income effect is positive, the good is inferior; if that positive effect exceeded 6.25 in absolute value, the good would be Giffen. Which mistake would change the reasoning in this example? Treating the Slutsky and Hicks compensations as identical. They coincide only for infinitesimal price changes; for a discrete change, state which method the question asks for. Signing the income effect wrongly. Ask Course Tutor: please explain this step from the example. Total effect = 12.5 − 25 = −12.5. Step 3: compensated income. Why does it follow? Add what you tried, so the explanation addresses your difficulty. Now try the source practice. With U = x^0.3 y^0.7, M = 200 and Px = 3, how much x is demanded? Pause before the answer. The source answer is: x = 0.3 times 200 / 3 = 20 units. Compare your reasoning as well as the result. If your response differs, return to the worked example and identify the step that needs correction. Explain the key idea in your own words, revisit any mistaken step, then continue to the next lesson. Use Stop to end Course Tutor when you finish.