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Gustavo Indart

THE DERIVATION OF DEMAND AND SUBSTITUTION AND INCOME EFFECTS Derivation of a Consumer’s Demand Assume: 1. Y represents all commodities other than X 2. Income and the price of Y are fixed 3. Preferences are given Given these assumptions, a change in the price of X → change in the quantity demanded of X We can therefore derive the demand functions by changing the price of X. First we draw Qy/Dx axes and below them the P/Qx axes to show the Demand curve Initially, we only know income and Py but this is sufficient to give us the Y-intercept ‘m/Py’ of the budget line. We then pick a price Px0 in the Demand diagram; this gives us the X-intercept and the budget line. Consumer equilibrium occurs at Xo where the budget line is tangent to the highest indifference curve. This quantity of X due to the price ‘Pxo’ is a quantity demanded of X and we have the first point on the demand function. We get the other points on the demand function by varying the price of X. Market Demand Definition: the quantities demanded by all individuals in the market at each price (sum of individual quantities demanded at each price) Example: suppose 10 individuals have individual demand described by P = 100 - 5q. What is market demand? Since Q = 10q, we know that q = Q/10. Substituting Q/10 for q in P = 100 - 5q, P = 100 - 0.5Q Substitution and Income Effects Substitution Effect: the effect of the relative change in price due to a price change with no income effect Income Effect: the effect of the change in absolute income due to the price change with no change in relative price Substitution and Income Effects of a Price Decrease The Substitution Effect of a change in price is always negative. The Income Effect depends upon whether the good is normal or inferior. If the good is an inferior good, the Substitution Effect and Income Effect move in the opposite direction (the Income Effect is positive) so that the demand for the good is likely to be inelastic. If the Substitution Effect has the same magnitude as the Income Effect for an inferior good, demand is vertical (perfectly
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