The following equations represent demand curves for a commodity, q: (i) q = 100 - p; (ii) q = 10 + p; (iii) q = 50. For each of these demands, calculate the choke price, the slope, and the price elasticities of demand in the neighborhood of q = 100 and q = 50.

Question

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(ii ) $\varepsilon$_Q,P= ($\Delta$Q/$\Delta$P)(P/Q) = (1/1)(110/100) = 1.1; (iii ) $\varepsilon$_Q,P= ($\Delta$Q/$\Delta$P)(P/Q) = undefined for q not equal to 50. At 50 we have: (i) $\varepsilon$_Q,P= (F1F1F1S1F1F1F10Q/F1F1F1S1F1F1F10P)(P/Q) = (-1/1)(50/50) = -1; (ii) $\varepsilon$_Q,P= ($\Delta$Q/$\Delta$P)(P/Q) = (1/1)(40/50) = .8; (iii) $\varepsilon$_Q,P= ($\Delta$Q/$\Delta$P)(P/Q) = 0 (since the change in quantity is zero for any price). Recall that the choke price is the price for which demand is zero. The slope of demand calculated algebraically is the coefficient of price (for a linear equation). Elasticity for this problem is defined as $\varepsilon$_Q,P= (F1F1F1S1F1F1F10Q/F1F1F1S1F1F1F10P)(P/Q). Graph the demands in order to get an idea of the choke price. Notice that demand (c) is vertical: there is no intersection of demand with the vertical axis. Hence, there is no choke price. Notice that the slope of demand is different if you read it off the graph than if you calculate it. This is because we tend to graph demand with price on the vertical axis and output on the horizontal axis (in other words, we graph demand as if P were on the left hand side of the equation and Q were on the right hand side). The graph is, to be precise, a picture of inverse demand. This question asks you for the slope of demand. This is $\Delta$Q/$\Delta$P. The price elasticity in the neighborhood of q = 100 must have q = 100 substituted into the demand equation so that we can calculate the corresponding price.

The Following Equations Represent Demand Curves for a Commodity, Q