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EC311 · Intermediate Microeconomics

EC311 / TOPIC 05

3.1 Engel curves and demand

How can one event move along an Engel curve while shifting a demand curve?

A variable on an axis creates movement along a curve; an off-axis variable shifts it.

Follow the cause and effect

  1. Derive Marshallian demand from the consumer problem.

  2. Vary income at fixed prices to trace the Engel curve.

  3. Vary own price at fixed income to trace the demand curve.

The model you are using

KEY MODEL
x=m/(2px)
y=m/(2py)
Engel at px=12:m=24x
demand at m=120:px=60/x
ηm=1

Conditions for this model

The shared experiment uses U=√(xy), positive prices and divisible goods. Engel holds both prices fixed; demand holds m and py fixed. The separate α=0.4 example is explicitly labelled.

The exam trap

Do not call an income change movement along demand because income is not on the P–Q axes.

Connect the reasoning to the graph

What changes

  • Higher income moves along Engel and, for a normal good, shifts demand right at the original price.

What stays fixed

The shared experiment uses U=√(xy), positive prices and divisible goods. Engel holds both prices fixed; demand holds m and py fixed. The separate α=0.4 example is explicitly labelled.

Keep these conditions throughout the comparison; change only what the case above specifies.

What to inspect

Vary own price at fixed income to trace the demand curve.

Compare before and after, and locate the conclusion on the graph.

5 MINUTES · TRANSFER THE IDEA

Can you explain it without the lesson?

Explain how Engel and demand respond when income elasticity is negative.

Lesson references

  • Varian, Intermediate Microeconomics, 8th ed., pp. 96–106 (PDF pp. 122–132); original linked income/price examples
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