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.)
To solve this question, we need to follow these steps:
1. Graph the supply and demand curves:
- The demand curve is given by: Qd = 4500 - 250P
- The supply curve is given by: Qs = 200P
2. Find the market equilibrium price and quantity by setting Qd equal to Qs:
- Set Qd = Qs: 4500 - 250P = 200P
- Solve for P: 4500 = 450P
- Divide both sides by 450: P = 10
- Substitute P value back into either Qd or Qs to find Q: Q = 4500 - 250(10) = 2000
- The equilibrium price is $10 and the equilibrium quantity is 2000 bushels.
3. Determine the target price and quantity:
- Given that the government wants a 10% increase in both price and quantity, we multiply the equilibrium values by 1.10:
- Target price = 10 * 1.10 = $11
- Target quantity = 2000 * 1.10 = 2200 bushels.
a) To determine the subsidy per bushel required:
- Calculate the price consumers would pay for 2200 bushels using the demand curve: Qd = 4500 - 250P
- Set Qd = 2200 and solve for P: 2200 = 4500 - 250P
- Solve for P: 250P = 4500 - 2200
- Divide both sides by 250: P = (4500 - 2200)/250 = 23
- Subtract the target price from this price to find the subsidy amount: Subsidy = 23 - 11 = $12 per bushel.
- Total cost on the government arising from the subsidy:
Total cost = Subsidy per bushel * Quantity = $12 * 2200 = $26,400.
b) To calculate the quantity of output the government would buy using a support price:
- Set Qs = 2200 and solve for P: 2200 = 200P
- Solve for P: P = 2200/200 = $11
- The government will buy the excess of quantity supplied (Qs) over quantity demanded (Qd) at the support price.
- Quantity government would buy = Qs - Qd = 2200 - 1750 = 450 bushels.
- Total cost to the government arising from the price support initiatives:
Total cost = Quantity bought * Support price = 450 * $11 = $4950.
c) To compare the net benefit derived by consumers from the subsidy price with the cost to taxpayers:
- The benefit to consumers is represented by the area under the demand curve between the prices of $11 and $9.2.
- Calculate the area: Area = (0.5 * subsidy per bushel * (Qd at support price - Qd at subsidy price)) + (subsidy per bushel * (Qd at support price - Qs))
Qd at support price = 1750 (from part b)
Qd at subsidy price = 1750 + (Qd at support price - Qs) = 1750 + (1750 - 2200) = 1300
- Calculate the area: Area = (0.5 * $12 * (1750 - 1300)) + ($12 * (1750 - 2200)) = $11,700.
- The cost to taxpayers of the subsidy price is the total cost on the government: $26,400.
In summary:
a) The subsidy per bushel would have to be $12, and the total cost on the government arising from the subsidy would be $26,400.
b) The government would buy 450 bushels, and the total cost to the government arising from its price-support initiatives would be $4950.
c) The extra net benefit derived by consumers from the subsidy price is $11,700, and the cost to taxpayers of the subsidy price is $26,400.