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Homework 2 Economics 503 Foundations of Economic Analysis Assigned: Week 2 Due: Week 3 1. We observe the income of the consumers of diamond rings increase by 10%. We observe that the equilibrium consumption of diamond rings goes up by 5%. Assume that nothing else happens to cause a change in the equilibrium in the diamond ring market. Explain why, we can infer that diamond rings are normal goods, but why we can’t say if they are income elastic luxury goods or income inelastic. Use at most 1 paragraph and 1 graph. If diamond rings are luxury goods, a 10% increase in income of diamond ring consumers will increase demand for diamond rings by more than 10% at any given price. If the supply curve is sufficiently inelastic, a shift in demand may lead to a sufficiently large rise in price such that actual diamonds purchase rises by less than 10%. However, if diamond rings were inferior goods, a rise in relevant income would result in lower demand at any price level, an effect that might be ameliorated to an extant by a decline in prices, but not completely offset to the extant that actual purchases would rise. S P 10% D′ D <10% Q 2. For reasons of safety, the Chinese government orders the closure of 75% of the coal mines currently operating in the PRC. Draw a graph of the effect of this on closure on the world coal market. Draw a graph of the effect of this on the world oil market. Explain your graphs in 1 paragraph or less. Closing most Chinese coal mines would be a large reduction in supply of coal at any price level. Coal supply would shift in. This would result in an increase in the equilibrium price of coal. Coal is a substitute for oil. An increase in the price of a substitute would cause the demand for oil to increase at any price level. In equilibrium, this would lead to a rise in the price oil. World Coal Market S′ P S D′ D Q P S World Oil Market D′ D Q 3. The demand for widgets is represented as QD = 100 – 8 P and the supply of widgets are given by QS = 40 + 4P. Calculate equilibrium price and quantity. Calculate the change in equilibrium price and quantity if a shift in the demand curve gives a demand schedule of QD = 124 – 8 P. The equilibrium price, P*, set quantity demanded equal to quantity supplied. 100 8P* 40 4 P* 60 12 P* P* 5 Q* 100 (8 5) 40 (4 5) 60 In other words, AS = 40, AD = 100, d = 8, s = 4 A D AS s d P* , Q* AD AS sd sd sd If AD increases to 124 then 124 8P* 40 4 P* 84 12 P* P* 7 Q* 124 (8 7) 40 (4 7) 68 4. Posit a simple demand curve for breakfast cereal of the form Q = 100 - 5P where Q is the quantity of breakfast cereal and P is the price per box. Calculate Q and Revenue (R) at each of the following price points. What is the price elasticity of demand as we move from price point to price point (use the mid point method)? What is the price point where revenue is largest? Explain why raising prices above that point does not increase revenues. 5 75 Revenue 375 6 70 420 7 65 455 Price Q 8 60 480 9 55 495 10 50 500 11 45 495 12 40 480 13 35 455 14 30 420 15 25 375 %ΔR/%ΔP Elasticity 0.622642 -0.37931 0.52 -0.48148 0.40107 -0.6 0.261538 -0.73913 0.095477 -0.90476 -0.10553 -1.10526 -0.35385 -1.35294 -0.66845 -1.66667 -1.08 -2.07692 -1.64151 -2.63636 ; At price = 10, revenue is largest. At lower prices, elasticity of demand is less elastic than -1. This means that a 1% rise in prices results in a less than 1% decline in demand which means that a price rise will increase revenue. At higher prices, demand becomes more elastic and raising prices above 10 results in bigger declines in demand offsetting higher prices and reducing revenue. 5. Below are short-term and long-term demand schedules for petroleum as well as a supply schedule. Assume that the supply schedule is the same in the long-term and the short-term. Calculate the equilibrium level of price and quantity for oil in the short and the long term within the range of $10 per barrel (Hint: the answer is the same for the short-term and the long-term). . Assume that a conflict in the Middle East permanently reduces the amount of oil that can be supplied at any price level. After the shock, only 94% of the previous level is supplied at any price level. Calculate the new supply schedules. Assuming the short-run and longrun demand curves are unchanged, calculate the new price of oil in the short-term and in the long-term (within a range of $10). P 60 70 80 90 100 110 120 130 140 150 QD QS ' Short-term Long-term 83,033.06 89,314.83 81,762.92 82,689.46 80,678.38 77,348.91 79,733.70 72,925.25 78,898.04 69,182.97 78,149.63 65,963.37 77,472.59 63,155.12 76,854.95 60,677.48 76,287.50 58,470.28 75,762.98 56,487.66 New 75256.27 76425.34 77452.7 78370.35 79200.43 79958.9 80657.67 81305.87 81910.65 82477.73 QS 80,059.86 81,303.55 82,396.49 83,372.72 84,255.78 85,062.66 85,806.03 86,495.60 87,138.99 87,742.26 The new supply curve is calculated by multiplying the old supply curve by .94 at every price point. Originally, demand is greater than supply whenever the price of oil is lower than $70. Supply is greater than demand whenever price is above $80. Equilibrium lies between $70 and $80. After the shock, demand is greater than supply in the short-run whenever price is below $90. Supply is greater than demand only when price is above $100. On the other hand, in the long-term, demand is less than new supply if the price is above $80. Therefore, the long-run price level is still in the same range that it was previous to the supply shock.