Suppose the US wheat market is represented by the following:
Demand Curve (D): P = 631.11 – 13.75Q
Supply Curve (S): P = 4Q
millions of metric tons: MMT
dollars per metric ton: $/MT
The x-axis represents the quantity of wheat in millions of metric tons and the y-axis represents the price of wheat in dollars per metric ton. No trade allowed, it means the quantity supplied must equal the quantity demanded.
a) Solve for the equilibrium free market quantity Q0 by setting the supply curve equal to the demand curve and solving for Q
b) Insert the answer from question a into the supply curve to find the free market equilibrium price P0
c) Use the y-axis intercept of the demand curve, the point (Q0,P0) and the intercept of the supply curve to create a graph with P labeled on the y-axis and Q labeled on the x-axis. Draw the supply curve by plotting two points (Q0,P0) and (0,0) then draw a line to connect them. Draw the demand curve by plotting two points (Q0,P0) and (0,631.11) then draw a line them. Make sure to label the demand curve (D) and the supply curve (S). Draw a vertical line from the x-axis to (Q0,P0) and then draw a horizontal line from the y-axis to (Q0,P0)
d) Calculate consumer surplus at the free market price and quantity (CS0) and please write the answer in the defined area of the graph
e) Calculate producer surplus at the free market price and quantity (PS0) and please write the answer in the defined area of the graph
f) Calculate total surplus (TS0) at the free market price and quantity by adding the two answers from question e and f together
g) If no trade is allowed, what would be the annual value of the US wheat economy at the free market price and quantity?
h) Suppose the US wheat market supply and demand curves are still the same but the government imposes a price floor for wheat P1 = $210.36/MT. Please find the quantity of wheat demanded (Q1) at the price floor P1 by inserting the price into the equation for the demand curve
i) Use the supply curve to find the marginal cost (P2) of producing Q1 in $/MT