Sugar Case answer
What does the world supply of sugar look like from the point of view of the U.S. market?
_The world supply of sugar looks perfectly elastic (horizontal) from the point of view of the U.S. market, at a price of 8.3 cents per pound. This conclusion comes from two statements in the case: "Annual world sales of sugar amount to roughly $100 billion" and "Thus, for our analysis the 2001 world price of 8.3 cents per pound is assumed to be constant outside the United States." In other words, because the U.S. sugar market is a small fraction of global sugar trade, we can reasonably assume that the U.S. is a price-taker in the world market, which means that it could import any quantity at the 2001 world price._
Derive the equations of the U.S. demand and supply curves for sugar, using the fact that you know one point on each curve and the elasticity at that point (assuming linear demand).
_Use the fact that the elasticity of demand at the 2001 equilibrium is -0.3._
_._
_Then solve Q = a - 0.285P using Q = 20.4 and P = 21.5_ _Q = 26.53 - 0.285P_ _._
_Similarly, use the fact that the elasticity of supply at the 2001 equilibrium is 1.5._
_._
_Then solve Q = a + 1.214P using Q = 17.4 and P = 21.5_ _Q = -8.70 + 1.214P._
_(Note that we carry the slopes of -0.285 and 1.214 out to three decimal places to conform to the treatment in the Pindyck & Rubinfeld text.)_
What would U.S. consumption and production of sugar be at the 8.3-cent world price? What would be the volume of imports?
_Plug P = 8.3 into the U.S. demand and supply equations to find that quantity demanded would be 24.2 billion pounds and quantity supplied would be 1.4 billion pounds (rounding). The difference is imports under free trade: 24.2 - 1.4 = 22.8 billion pounds. These points are labeled in the graph below (not drawn to scale)._
_Imports = 22.8_
1.4 24.2 Q
(billions of pounds)
DUS
SUS
P
(cents/pound)
8.3
Just for the sake of comparison, what would price and consumption of sugar be if imports
_The world supply of sugar looks perfectly elastic (horizontal) from the point of view of the U.S. market, at a price of 8.3 cents per pound. This conclusion comes from two statements in the case: "Annual world sales of sugar amount to roughly $100 billion" and "Thus, for our analysis the 2001 world price of 8.3 cents per pound is assumed to be constant outside the United States." In other words, because the U.S. sugar market is a small fraction of global sugar trade, we can reasonably assume that the U.S. is a price-taker in the world market, which means that it could import any quantity at the 2001 world price._
Derive the equations of the U.S. demand and supply curves for sugar, using the fact that you know one point on each curve and the elasticity at that point (assuming linear demand).
_Use the fact that the elasticity of demand at the 2001 equilibrium is -0.3._
_._
_Then solve Q = a - 0.285P using Q = 20.4 and P = 21.5_ _Q = 26.53 - 0.285P_ _._
_Similarly, use the fact that the elasticity of supply at the 2001 equilibrium is 1.5._
_._
_Then solve Q = a + 1.214P using Q = 17.4 and P = 21.5_ _Q = -8.70 + 1.214P._
_(Note that we carry the slopes of -0.285 and 1.214 out to three decimal places to conform to the treatment in the Pindyck & Rubinfeld text.)_
What would U.S. consumption and production of sugar be at the 8.3-cent world price? What would be the volume of imports?
_Plug P = 8.3 into the U.S. demand and supply equations to find that quantity demanded would be 24.2 billion pounds and quantity supplied would be 1.4 billion pounds (rounding). The difference is imports under free trade: 24.2 - 1.4 = 22.8 billion pounds. These points are labeled in the graph below (not drawn to scale)._
_Imports = 22.8_
1.4 24.2 Q
(billions of pounds)
DUS
SUS
P
(cents/pound)
8.3
Just for the sake of comparison, what would price and consumption of sugar be if imports