Consider the following demand and supply functions for milk:
Q d = 300 - 100P
Q s = 50P
where P is price (in dollars) and Q d and Q s are the quantity demanded and quantity supplied of milk (in thousands of 4-litre bags), respectively.
i) Find the equilibrium price and quantity of milk.
ii) Suppose the government offers a subsidy to milk producers equal to 30¢ for each 4-litre bag of milk sold. Find the new equilibrium price and quantity under this policy. Describe the incidence of the subsidy by giving the exact dollar amounts. (Note: You must provide an algebraic answer for this part. A diagrammatic answer will receive only partial credit.)
iii) Return to the original question (i.e., ignore what takes place in part ii)). Now suppose the government offers a subsidy to consumers equal to 10¢ for each 4-litre bag of milk bought. Describe the incidence of the subsidy now. (Again, provide an algebraic answer.)Consider the following demand and supply functions for milk: Q d = 300 - 100P Q s = 50P where P is price (in dollars) and Q d and Q s are the quantity demanded and quantity supplied of milk (in thousands of 4-litre bags), respectively. (5) i) Find the equilibrium price and quantity of milk.
ii) Suppose the government offers a subsidy to milk producers equal to 30¢ for each 4-litre bag of milk sold. Find the new equilibrium price and quantity under this policy. Describe the incidence of the subsidy by giving the exact dollar amounts. (Note: You must provide an algebraic answer for this part. A diagrammatic answer will receive only partial credit.)
iii) Return to the original question (i.e., ignore what takes place in part ii)). Now suppose the government offers a subsidy to consumers equal to 10¢ for each 4-litre bag of milk bought. Describe the incidence of the subsidy now. (Again, provide an algebraic answer.)
A) At equilibrium, demand = supply
That is, 300-100P = 50P
Or, 300 = 150P
Or, P* = $2 ; Q* = 100 thousand
B) Now, milk producers get a subsidy of 30 cents for each bag milk sold
Thus, new supply curve equation: P=(Q/50) - 0.3
Or, 50P = Q - 15
Or, Q = 50P + 15
Thus, new equilibrium would be:
300-100P = 50P+15
285 = 150P
P' = $1.9 and Q' = 110 thousand
So, Consumer pays $1.9 and producer receives $1.9+$0.3 = $2.2
So, incidence on consumers = $2-$1.9 = $0.10
Incidence on producers = $2.2 - $2 = $0.20
Incidence on government = $0.3*110 = $33 thousand
C) Now consumers receive subsidy of $0.10
So, new demand curve equation would be: P = (3 - 0.01Q) - 0.1
Or, 100P = 300-Q-10
100P = 290-Q
Or, Q = 290-100P
So, new equilibrium would be:
290-100P = 50P
290 = 150P
Or, P'' = $1.933
So,
Incidence on buyers = $2-$1.93 = $0.07
Incident on sellers = $0.1-$0.07 = $0.03
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