1F The Derivation of Demand and Substitution and Income Effects

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Gustavo Indart

THE DERIVATION OF DEMAND AND SUBSTITUTION AND INCOME EFFECTS Demand is usually downward sloping and Supply upward sloping Intersection of Demand and Supply curves is the equilibrium point Change in quantity demanded/quantity supplied are movements along the demand/supply curve and change in the demand/supply is a shift of the demand/supply curve The Demand/Supply Curve is the sum of Individual demand/supply of the product Factors that Shift Demand: 1. Taxes/Subsidies. 2. Change in Prices of related goods (Substitutes/Complementary Goods) 3. Change in Income 4. Change in Preferences Factors That Shift Supply 1. Prices of Inputs (as prices rise, Supply falls) 2. Number of Firms (as firms rise, Supply rises) 3. Technology (a new breakthrough increases supply) 4. Taxes/Subsidies - Price Floor is a Minimum Price the government sets for a product o Usually causes shortage because Qd>Qs (e.g Minimum Wage) - Price Ceiling is a Maximum Price the government sets for a product. o Usually causes an excess supply as Qs>Qd - Price Controls are economically inefficient 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 inelastic). If the Income Effect has a greater magnitude than the Substitution Effect, demand is positive sl
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