The market demand for cars is P = 1000 - Q and the supply is P = 100 + 2Q. A quota of 150 units will create a dead weight loss of:

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The deadweight loss (DWL) from a quota can be calculated as the area of the triangle formed by the demand curve, the supply curve, and the quantity after the quota. First, find the equilibrium price and quantity without the quota by setting demand equal to supply: $1000 - Q = 100 + 2Q$, solving for Q gives $Q = 300$. The equilibrium price (P) is found by substituting Q back into either the demand or supply equation, $P = 100 + 2(300) = 700$. With a quota of 150 units, the quantity is reduced from the equilibrium quantity of 300 units. The price consumers are willing to pay for the 150th unit is found by substituting Q = 150 into the demand equation, $P = 1000 - 150 = 850$. The price suppliers are willing to accept for the 150th unit is found by substituting Q = 150 into the supply equation, $P = 100 + 2(150) = 400$. The DWL is the area of the triangle with a base of 150 units (300 - 150) and a height of 450 (850 - 400). The area of a triangle is $0.5 \times base \times height$, so the DWL = $0.5 \times 150 \times 450 = 33750$.

The Market Demand for Cars Is P = 1000 -