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hi guys, im stuck on this question, if anyone can help me out i would really appreciate it !

Q: The market demand and supply curves for an agricultural product are as follows:

Qd = 4500-250P and Qs = 200p

where quantities are in thousands of bushels per annum and price is in dollars per bushel.

the government wishes to acheive a higher point on the supply curve than the initial equilibrium. the desired point would involve both price and quantity being 10% greater that their initial equlibrium levels. the government is considerting either a subsidary or support price.

a) if the subsidary were used, how much would the subsidery per bushel have to be ? what would be the total cost on the government arising from this subsidary?

b) if the support price were used, what quantity of output would the government buy? what would be the total cost to the government arising from its price supporting initiatives ?

c) compared to the supprt price, what is the extra net benifit derived by consumers from the subsidary price ? what is the cost to taxpayers of the subsidary price ?

thanx in advance !

First, graph your supply and demand curves. Next, solve for the market equilibrium price and quantity; set Qd=Qs. I get P=10,Q=2000. Lable these on your graph. From this, the target price and quantity are P=11 and Q=2200.

a) A subsidy (to consumers) would take the form of a fixed per-unit amount given to consumers. (This effectively makes a vertical increase in the demand curve.) Calculate the price consumers would pay for 2200 bushels. (I get $9.2). So, the subsidy needed is 11-9.2 = $1.8 per bushel. Cost to government is 1.8*2200=?

b) With a support price, government sets the price, in this case $11., and buys the excess of quantity supplied less quantity demanded at this price. You know quantity supplied at $11 is 2200. Calculate quantity demanded at $11. (I get 1750). Thus, the government will buy 450 bushels at $11 each.

c) The benefit to consumers, going from a support price (which benefits producers) to a subsidary price (which benefits consumers) is represented by the area under the demand curve between the prices of $11 and $9.2 (1.8*1750 + .5*1.8*450).

I calculate that taxpayers gain by going from a support price to a subsidy (unless, under a support price, the government finds a practical use for all the grain it buys.)

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