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# ch8lec - ECON 306 Chapter 8 The Slutsky Equation RUST CHO...

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ECON 306 Chapter 8: The Slutsky Equation RUST, CHO, DIAZ

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Introduction The Slutsky Equation decomposes the total change in demand caused by a change in prices into two pieces, the Substitution effect and the Income effect. What happens when the price of a good changes? Assume that the price of x 1 goes down from p 1 to p 1 : 1) Good x 1 becomes cheaper relative to other goods. The price ratio p 1 / p 2 (or the relative price) goes down so the new budget line becomes flatter. 2) Consumer’s purchasing power changes as well. Some bundles that were unfeasible before are affordable now. Look first at the movements in the budget constraint as the price of x 1 goes down (Fig 8.1). Pivot: changes the relative price (the slope) leaving the purchasing power constant (so the consumer can afford exactly the initial bundle). Shift: changes the purchasing power leaving the relative price constant.
08.01

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The Substitution effect The Substitution effect measures the change in the demand of a good caused by a change in the relative price keeping the purchasing power constant. This isolates the pure effect from changing the relative price. Why do we need to keep the purchasing power constant? When the price of a good decreases (increases) the consumer’s purchasing power increases (decreases). 1) For normal goods, the increase in purchasing power allows the consumer to increase further the demand for the good. 2) For inferior goods consumer reduces quantity demanded as the purchasing power increases. If we allow the purchasing power to change, we confound the change in demand caused by the change in the relative price (the good becomes cheaper or more expensive) with the change caused by a higher or lower “real income”. So, we need consumers facing the new price ratio while maintaining the original demanded bundle just affordable.
The Substitution effect (cont.) How to keep the purchasing power constant? We need to compensate the consumer after the price change such that the original bundle is just affordable. This implies to find a new amount of money m ’ such that the original bundle is affordable at the new set of prices. The original bundle X =( x 1 , x 2 ) must satisfy both m ’= p’ 1 x 1 + p 2 x 2 and m = p 1 x 1 + p 2 x 2 .

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