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Homework_9_Solutions

Homework_9_Solutions - Problem 1 Suppose that the domestic...

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Problem 1 Suppose that the domestic supply of oil and domestic demand for oil are given by the following functions: Q S = 10 + 3P and Q D = 100 - 2P where quantity is measured in millions of barrels and price in dollars per barrel. a) What is the domestic market-clearing price per barrel of oil? What is the quantity associated with this price? Illustrate your answer in a diagram. 64 * 64 ) 18 ( 2 100 18 * 18 5 90 2 100 3 10 Q Q P P P P Q Q d s Suppose that the world price of oil is $10 per barrel. If there are no barriers to trade then the domestic price will equal the world price of $10. b) At this price what is the domestic demand? What is the domestic supply? What is the demand for imports? Illustrate your answer in a diagram. 40 5 90 3 10 2 100 40 ) 10 ( ) 10 ( 3 10 ) 10 ( 80 ) 10 ( ) 10 ( 2 100 ) 10 ( d I d I s d d I s s d d Q P Q P P Q Q Q imports for Demand P Q P Q P Q P Q P Barrels of oil 64 18
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Suppose that the government decides to subsidize domestic oil producers at $2 per barrel. c) Given the subsidy how much oil will domestic suppliers provide? What is the change in the demand for imports? 46 ' ) 10 ( 3 16 ' 10 3 16 ' ) 2 ( 3 10 ' 2 3 10 s s w s s s s s Q Q P if P Q P Q Subsidy P Q P Barrels of oil 64 18 P w =10 40 80 imports P Barrels of oil 64 18 P w =10 40 80 Q s subsidy Q s 46 Imports w/Subsidy
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d) What will be the gain to domestic suppliers (that is what is the change in producer surplus)? What is the cost of the subsidy program to the government? What is the deadweight loss? Illustrate the change in producer surplus, the cost of the program and the deadweight loss in a diagram. 6 92 86 : 92 46 * 2 : 86 2 2 ) 40 46 ( 2 : c DWL c b Government to Cost h b B b PS P Barrels of oil 64 18 P w =10 40 80 Q s subsidy Q s 46 12 a b c Original Producer Surplus = a Producer Surplus with Subsidy = a+b Change in PS = b Cost to government=b+c DWL=c
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2. In class we discussed the market for natural gas represented by the following supply and demand curves: Q D (P G ,P O ) = -5P G + 3.75 P O and Q S (P G ,P O ) = 14 + 2P G +.25P O where P G and P O are the prices of natural gas (in $ per mcf) and oil (in $ per barrel) and quantity of natural gas is measured in tcf. Adapt the procedure developed in class used to calculate the incidence of a tax to find an expression for the derivative of the market clearing price of gas with respect to the price of oil in terms of the derivatives of supply and demand for natural gas with respect to both prices. Using the specific values for the derivatives of supply and demand with respect to prices
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