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Math Help - help with this question please

  1. #1
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    Red face help with this question please

    I am stuck with this question. im hoping someone can lead me to an answer

    The Federal Government is considering increasing the sales tax on petrol by $.03 per litre. Last year motorists purchased 10 million litres of petrol per month. The demand curve is such that every $.01 increase in price decreases sales by 100,000 litres per month. You also know that for every $.01 increase in price, producers are willing to provide 50,000 more gallons of gasoline to the market. The Government has stated that the $.03 tax will increase government revenues by $300,000 per month and raise the price of gasoline by $.03 per litre. Is this correct?
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  2. #2
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    The government's claim is predicated on the demand sticking at 10M per month (quelle surprise ). Does your given demand curve info support or refute that assumption?

    BTW, the supply curve info is just a smokescreen for purposes of this question...any additional tax is an additional cost to Buyer, but not additional revenue to Supplier.
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  3. #3
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    Hi Lochwulf,
    Thanks heaps for your prompt reply!
    Unfortunately I have not been given a demand curve for this question. So im not too sure how about to answer this question :S
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  4. #4
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    True, you don't have the complete demand curve function in its customary form, but you are given enough of it to answer the question; viz: "The demand curve is such that every $.01 increase in price decreases sales by 100,000 litres per month..."

    The government's claim that the new tax will boost total gov't revenue by 300K rests on the assumption that current demand remains unchanged following the tax hike: 10M x 0.03 = 300,000.

    The question is only asking whether or not the government's claim is correct....you don't have to come up with the new equilibrium point. Remembering that to a consumer, tax increase = price increase, you have all you need for the answer. Cheers!
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  5. #5
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    Thanks Lochwulf!
    The question does make more sense, however I am still confused about the actual answer for this question.
    i.e how to write it up?

    I am assuming that my teacher would also like a graph to support this claim as well.
    Would you be able to help me with this?

    Thanks heaps
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  6. #6
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    As strictly stated, the question is simply asking if the government's claims are correct. If you need to support your answer with a graph, then start with a generic supply / demand graph. The given elasticity info tells you that the curves are pretty typical...Supply slopes up; Demand slopes down; and they're linear, at least over a relevant range.

    Mark the 'pre-tax' equilibrium price and quantity on the axes. Show the points only; you don't have the info to determine the specific equilibrium price, anyway (nor will it be needed).

    Next, draw in a second demand line, showing how the demand curve shifts as a result of a tax increase.

    Now mark on the axes the new 'post-tax' equilibrium P and Q.

    Finally, the assertion that total gov't revenue would increase by 300K is true only if the equilibrium Q remained unchanged after the tax increase. Does it? (If the equilibrium quantity moves, it means the new 0.03 tax will be imposed on some quantity other than 10M litres; thus the additional revenue will not equal 300K.)

    Second, the claim that the effective price to consumers would rise by exactly the tax increase (0.03 / litre) is true only if the post-tax equilibrium price remains unchanged vs. the pre-tax equilibrium price* ...does it?

    *(Suppose, e.g., that something costs 1.00 before a tax hike. After the imposition of a new 0.05 sales tax per unit, let's say the equilibrium price drops to 0.98. Now the total cost to the consumer is 1.03, including the tax...hence, the "price" (to the consumer) does not increase by precisely the amount of the new tax.)

    Again, your generic graph can show these dynamics with using specific prices, which you don't know anyway.
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