QuestionMay 29, 2025

3. Suppose the market for organically grown wheat is modeled through the following market supply and demand functions: P=10+0.5Q_(s) and P=22-2.5Q_(D) where Q_(S) and Q_(D) are in millions of bushels,and P is price per bushel. a. Find the market equilibrium price, P_(E) and market equilibrium quantity, Q_(E) b. Now determine the value of producer surplus and consumer surplus at equilibrium.

3. Suppose the market for organically grown wheat is modeled through the following market supply and demand functions: P=10+0.5Q_(s) and P=22-2.5Q_(D) where Q_(S) and Q_(D) are in millions of bushels,and P is price per bushel. a. Find the market equilibrium price, P_(E) and market equilibrium quantity, Q_(E) b. Now determine the value of producer surplus and consumer surplus at equilibrium.
3. Suppose the market for organically grown wheat is modeled through the following market supply and demand functions: P=10+0.5Q_(s) and P=22-2.5Q_(D) where Q_(S) and Q_(D) are in millions of bushels,and P is price per bushel. a. Find the market equilibrium price, P_(E) and market equilibrium quantity, Q_(E) b. Now determine the value of producer surplus and consumer surplus at equilibrium.

Solution
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Answer

Equilibrium Price, P_{E} = 12; Equilibrium Quantity, Q_{E} = 4 million bushels. ### Consumer Surplus = 20 million dollars; Producer Surplus = 4 million dollars. Explanation 1. Set Supply Equal to Demand Equate 10 + 0.5Q_{s} = 22 - 2.5Q_{D} and solve for Q. 2. Solve for Equilibrium Quantity Since Q_{s} = Q_{D} = Q_{E}, solve 10 + 0.5Q_{E} = 22 - 2.5Q_{E}. Rearrange to get 3Q_{E} = 12, so Q_{E} = 4 million bushels. 3. Solve for Equilibrium Price Substitute Q_{E} = 4 into either supply or demand equation. Using supply: P_{E} = 10 + 0.5 \times 4 = 12. 4. Calculate Consumer Surplus Consumer surplus is the area of the triangle above price and below demand curve: \frac{1}{2} \times (22 - 12) \times 4 = 20 million dollars. 5. Calculate Producer Surplus Producer surplus is the area of the triangle below price and above supply curve: \frac{1}{2} \times (12 - 10) \times 4 = 4 million dollars.

Explanation

1. Set Supply Equal to Demand<br /> Equate $10 + 0.5Q_{s} = 22 - 2.5Q_{D}$ and solve for $Q$.<br /><br />2. Solve for Equilibrium Quantity<br /> Since $Q_{s} = Q_{D} = Q_{E}$, solve $10 + 0.5Q_{E} = 22 - 2.5Q_{E}$.<br /> Rearrange to get $3Q_{E} = 12$, so $Q_{E} = 4$ million bushels.<br /><br />3. Solve for Equilibrium Price<br /> Substitute $Q_{E} = 4$ into either supply or demand equation. Using supply: $P_{E} = 10 + 0.5 \times 4 = 12$.<br /><br />4. Calculate Consumer Surplus<br /> Consumer surplus is the area of the triangle above price and below demand curve: $\frac{1}{2} \times (22 - 12) \times 4 = 20$ million dollars.<br /><br />5. Calculate Producer Surplus<br /> Producer surplus is the area of the triangle below price and above supply curve: $\frac{1}{2} \times (12 - 10) \times 4 = 4$ million dollars.
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