Suppose that the market for milk can be represented by the following.
Demand: P=12_0.5QD
Supply: P: 0.1QS
Where P is the price per gallon, and Q represents quantity of milk, represented in millions of gallons of milk consumed per day.
i. Calculate the equilibrium price and quantity of milk
ii. To help dairy farmers, the government sets a minimum price of k2.50 per gallon of milk. What is the new quantity of milk sold in the market place?
iii. Illustrate your answer (i) and (ii) on a graph
iv. Using this graph, calculate how the consumer surplus and producer surplus change after the price supports are enacted.
v. Suppose that the government supports the k2.50 per gallon price by purchasing any excess milk suppliers make available but the are unable to sell to the consumers. How much milk must the government buy
Answer all the questions accordingly in detailed nicely
i. To find the equilibrium price and quantity of milk, we need to set the demand equal to the supply:
12 - 0.5Q = 0.1Q
12 = 0.6Q
Q = 20
Now plug Q back into either the demand or supply equation to find the equilibrium price:
P = 12 - 0.5(20)
P = 12 - 10
P = $2 per gallon
So, the equilibrium price of milk is $2 per gallon and the equilibrium quantity is 20 million gallons.
ii. With a minimum price of $2.50 per gallon set by the government, the quantity demanded will be less than the quantity supplied. To find the new quantity of milk sold, set the minimum price equal to the demand equation:
2.50 = 12 - 0.5QD
QD = (12 - 2.50) / 0.5
QD = 9.5 / 0.5
QD = 19
So, with a minimum price of $2.50 per gallon, the new quantity of milk sold is 19 million gallons.
iii. I am unable to illustrate the graph for you at this time, but I encourage you to graph the supply and demand equations to see where they intersect at equilibrium price and quantity, and then see how the minimum price affects the quantity sold.
iv. Consumer surplus is the area between the demand curve and the equilibrium price, while producer surplus is the area between the supply curve and the equilibrium price. When the government sets a minimum price of $2.50 per gallon, this creates a shortage of milk, reducing consumer surplus and increasing producer surplus.
v. To find out how much milk the government must buy to support the $2.50 per gallon price, we look at the difference between the new quantity demanded and the new quantity supplied:
Quantity demanded = 19 million gallons
Quantity supplied = 0.1Q
Quantity supplied = 0.1(20)
Quantity supplied = 2 million gallons
The government must buy the difference between the quantity demanded and supplied:
Government purchase = 19 - 2
Government purchase = 17 million gallons
Therefore, the government must buy 17 million gallons of milk to support the $2.50 per gallon price.