1.Suppose that the market for milk can be represented by the following equations
Demand: p=12-0.5 QD
Supply: p=0.1 QS
Where P is the price per gallon, and Q represent quantity of milk, represent in millions of gallons of milk consumed per day.
A. Calculate the equilibrium price and quantity of milk.
B. 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.
C. Illustrate your answer to (A) and (B) on a graph.
D. Using this graph, calculate how the consumer surplus and producer surplus change after the price supports are enacted.
E. Suppose that the government supports the k2.50 per gallon price by purchasing an excess milk supplies make available but are unable to sellto consumers. How much milk must the government buy.
(Assignment form)
A. To find the equilibrium price and quantity of milk, we need to set the demand equal to the supply and solve for Q:
12-0.5Q = 0.1Q
12 = 0.6Q
Q = 20
Now that we have the quantity, we can plug it back into either the demand or supply equation to find the equilibrium price:
p = 12 - 0.5(20)
p = 12 - 10
p = 2
Therefore, the equilibrium price is k2 per gallon and the equilibrium quantity is 20 million gallons per day.
B. With a minimum price of k2.50 per gallon, we can set the new price equal to k2.50 and solve for the new quantity:
k2.50 = 0.1QS
QS = 25
Therefore, the new quantity of milk sold in the market is 25 million gallons per day.
C. (Graph to be illustrated)
D. Consumer surplus is the area above the price line and below the demand curve, while producer surplus is the area below the price line and above the supply curve. When price supports are enacted and the price is increased to k2.50, consumer surplus decreases as consumers are now paying more for milk, while producer surplus increases as producers are now receiving a higher price for their milk.
E. To find out how much milk the government must buy to support the k2.50 price, we need to find the difference between the new quantity demanded at that price and the original equilibrium quantity:
25 - 20 = 5
Therefore, the government must buy 5 million gallons of milk to support the k2.50 price.