Suppose the market demand function in a certain market where Q is measured in thousands of units is Q^d = 20 - 2.5P,and the market supply function is Q^s = 2.5P - 7.5.How much deadweight loss would there be in this market if the quantity bought and sold was 8,500 units? A) $2.03 B) $4.05 C) $1,800 D) $2,025

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To calculate the deadweight loss, we first need to find the equilibrium price and quantity. Setting the demand and supply functions equal to each other:$$20 - 2.5P = 2.5P - 7.5$$Solving for $P$, we get:$$20 + 7.5 = 2.5P + 2.5P$$$$27.5 = 5P$$$$P = 5.5$$Plugging $P = 5.5$ into either the demand or supply equation to find the equilibrium quantity ($Q$):$$Q = 20 - 2.5(5.5) = 20 - 13.75 = 6.25$$ (in thousands of units)The equilibrium quantity is 6,250 units, but the quantity bought and sold is 8,500 units, which is 2,250 units more than the equilibrium quantity. This discrepancy indicates a deadweight loss due to inefficiency.To calculate the deadweight loss, we need to find the area of the triangle formed by the overproduction. The base of the triangle is the difference in quantity (2,250 units), and the height is the difference between the price consumers are willing to pay at that quantity and the price producers are willing to accept.From the demand function, the price consumers are willing to pay for 8.5 thousand units can be found by rearranging the demand equation to solve for $P$ when $Q = 8.5$:$$8.5 = 20 - 2.5P$$$$2.5P = 20 - 8.5$$$$2.5P = 11.5$$$$P = 4.6$$From the supply function, the price producers are willing to accept for 8.5 thousand units:$$8.5 = 2.5P - 7.5$$$$2.5P = 8.5 + 7.5$$$$2.5P = 16$$$$P = 6.4$$The height of the triangle is the difference in these prices, $6.4 - 4.6 = 1.8$. The area of the triangle, which represents the deadweight loss, is:$$\frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 2.25 \times 1.8 = 2.025$$Since the quantities are in thousands and the price is in dollars, the deadweight loss is $2.025 \times 1,000 = \$2,025$.

Suppose the Market Demand Function in a Certain Market Where