The market demand and supply curves for an agricultural product are as
follows:
Qd = 4,500 - 250P; Qs = 200P
where quantities are in thousands of bushels per annum and price is in dollars
per bushel.
The government wishes to achieve a higher point on the supply curve than the
initial equilibrium. The desired point would involve both price and quantity
being 10% greater than their initial equilibrium levels. The government is
considering either a subsidy or a support price.
(a) If the subsidy were used, how much would the subsidy per bushel have
to be? What would be the total cost to the government arising from
this subsidy?
(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 support price, what is the extra net benefit derived by
consumers from the subsidised price? What is the extra cost to
taxpayers of the subsidised price?
A person named "me" posted this same question on October 10. See my post.
Certainly! Let's break down each part of the question:
(a) If a subsidy were used, the government would provide a financial incentive to agricultural producers per bushel of the product. The subsidy would be designed to increase the supply and decrease the price to achieve the desired point on the supply curve.
To find the subsidy per bushel, we need to calculate the difference in price between the initial equilibrium and the desired point. Let's denote the initial equilibrium price as P1 and the desired price as P2. Since the desired price is 10% greater than the initial equilibrium price, we have:
P2 = 1.1 * P1
Next, we need to find the corresponding quantities at both prices. Using the demand and supply curves, we equate the quantities demanded (Qd) and supplied (Qs) at each price:
For P1:
Qd = 4,500 - 250 * P1
Qs = 200 * P1
For P2:
Qd = 4,500 - 250 * P2
Qs = 200 * P2
Since we want the quantities at the desired point to be 10% greater than those at the initial equilibrium, we can write:
Q2 = 1.1 * Q1
Now we have a system of equations that we can solve to find the subsidy per bushel and the total cost to the government. By substituting the equations and solving the system, we can determine the numerical values required.
(b) If a support price were used, the government would set a minimum price at which agricultural producers can sell the product. This would provide a price floor to support the market and maintain a higher point on the supply curve.
To find the quantity of output the government would buy, we need to determine the point on the supply curve where the quantity supplied equals the desired level. Using the supply curve equation Qs = 200P, we can substitute the desired quantity (1.1 * Q1) and solve for the price (P2) at that quantity.
The total cost to the government arising from its price support initiatives would be the quantity of output purchased multiplied by the support price.
(c) To compare the support price and the subsidized price, we need to calculate the differences in net benefit and cost.
The extra net benefit derived by consumers from the subsidized price can be found by calculating the difference in consumer surplus between the subsidized price and the support price. Consumer surplus represents the difference between what consumers are willing to pay for a product and what they actually pay.
The extra cost to taxpayers of the subsidized price can be obtained by calculating the difference in producer surplus between the subsidized price and the initial equilibrium price. Producer surplus represents the difference between the price at which producers are willing to supply a product and the price they actually receive.
By comparing these values, we can determine the extra net benefit derived by consumers and the extra cost to taxpayers resulting from the subsidized price.
Overall, solving the equations and performing the necessary calculations will provide the specific numerical values and answers required for each part of the question.