Question

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.)

Answer #1

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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