3. UYGULAMA DERS� SORU VE CEVAPLARI

3. UYGULAMA DERS� SORU VE CEVAPLARI - 12. Suppose that...

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SD&ZY_2010-2011/3 12. Suppose that the long-run world demand and supply elasticities of crude oil are -0.906 and 0.515, respectively. The current long-run equilibrium price is $30 per barrel and the equilibrium quantity is 16.88 billion barrels per year. Derive the linear long-run demand and supply equations. Next, suppose the long-run supply curve you derived above consists of competitive supply and OPEC supply. If the long-run competitive supply equation is: 7.78 0.29 , = + C S P what must be OPEC's level of production in this long-run equilibrium? Solution: If the demand curve is linear, it is in the form of . = + D Q a bP Also, we know that 16.88 0.906 0.510. 30 = ⇔ = = - = - P Q E b b E Q P Rearranging the linear expression for demand allows us to solve for a as follows: 16.88 0.510(30) 32.180. = - = + = D a Q bP a We may now write the linear expression for demand as 32.18 0.510 . = - D Q P If the supply curve is linear, it is in the form of . = + S Q c dP Also, we know that 16.88 0.515 0.290. 30 = = = = P Q E d d E Q P Rearranging the linear expression for demand allows us to solve for c as follows: 16.88 0.290(30) 8.18. = - = - = S c Q dP c We may now write the linear expression for supply as 8.18 0.290 . = + S Q P OPEC's supply is the difference between the world supply and competitive supply at $30. We know that world supply at $30 is 16.88. Competitive supply at $30 is ( ) 7.78 0.29 30 16.48. + = This implies that OPEC's supply is 0.4 billion barrels per year at $30 in this long-run equilibrium. 13. Harding Enterprises has developed a new product called the Gillooly Shillelagh. The market demand for this product is given as follows: Q = 240 - 4P a. At what price is the price elasticity of demand equal to zero? b. At what price is demand infinitely elastic? c. At what price is the price elasticity of demand equal to one? d. If the shillelagh is priced at $40, what is the point price elasticity of demand? Solution: The demand curve given in this problem is linear. The intercepts of the inverse demand curve on the price and quantity axes are $60 and 240 respectively. The price elasticity of demand varies along the length of this demand curve. Demand is infinitely elastic at the intercept on the price axis. Demand is completely inelastic at the intercept on the quantity axis. Demand is unit elastic at the half-way point between these two extremes. a.
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This note was uploaded on 06/13/2011 for the course ECON 2450 taught by Professor Appo during the Spring '11 term at Michigan Flint.

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3. UYGULAMA DERS� SORU VE CEVAPLARI - 12. Suppose that...

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