1. Assume a colleague at the ERS estimated the following demand and supply equat
ID: 1202537 • Letter: 1
Question
1. Assume a colleague at the ERS estimated the following demand and supply equations for rice in the U.S.
Q = 100 – 4P
Q = 10 +2P
Where: Q = Quantity (lbs), P= Price (cents/lb)
a. Calculate the equilibrium price and quantity of rice in the U.S.
Assume you estimated the following demand and supply equations for U.S. rice in South Korea.
Q= 70- 2P
Q = 10 + 1P
Where: Q = Quantity (lbs), P= Price (cents/lb)
b. Calculate the equilibrium price and quantity for South Korea
c. Lets allow trading to occur between the U.S. and South Korea. Please calculate the quantity in the trade sector (the market clearing quantity in the trade sector) and the market clearing price (the equilibrium price between the two countries). (Hint: you will first need to calculate the excess supply in the U.S. and the excess demand in South Korea
Explanation / Answer
Ans. (a)
Q = 100 – 4P .........(1)
Q = 10 +2P .........(2)
Where: Q = Quantity (lbs), P= Price (cents/lb)
From equaltion (1) we get inverse demand function as P = 25 - (Q / 4) ...........(3)
From equaltion (2) we get inverse supply function as P = (Q / 2) - 5 ...........(4)
At equilibrium demand = supply
=> 25 - (Q / 4) = (Q / 2) - 5
=> - (Q / 4) - (Q / 2) = - 5 - 25
=> 3Q / 4 = 30
=> 3Q = 120
=> Q = 40 ..........(5)
Puting equaltion (5) into equaltion (3), we get
P = 25 - (Q / 4) = 25 - (40 / 4) = 25 - 10 = 15
=> P = 15
Hence, the equilibrium price and quantity of rice in the U.S are 15 and 40 respectively.
Ans. (b)
Q = 70 – 2P .........(6)
Q = 10 +1P .........(7)
Where: Q = Quantity (lbs), P= Price (cents/lb)
From equaltion (1) we get inverse demand function as P = 35 - (Q / 2) ...........(8)
From equaltion (2) we get inverse supply function as P = Q - 10 ...........(9)
At equilibrium demand = supply
=> 35 - (Q / 2) = Q - 10
=> - (Q / 2) - Q = - 10 - 35
=> 3Q / 2= 45
=> 3Q = 90
=> Q = 30 ..........(10)
Puting equaltion (10) into equaltion (8), we get
P = 35 - (Q / 2) = 35 - (30 / 2) = 35 - 15 = 20
=> P = 20
Hence, the equilibrium price and quantity of U.S rice in South Korea are 20 and 30 respectively.
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