QuestionAugust 9, 2025

A price floor is given along with demand and supply functions, where D(q) is the price, in dollars per unit, that consumers will pay for qunits, and S(q) is the price, in dollars per unit, at which producers will sell qunits. Find (a)the equilibrium point, ( (b) the point (q_(F),p_(F)) (c) the new consumer surplus, (d) the new producer surplus, and (e)the deadweight loss. D(q)=110-1.25q,S(q)=10+0.75q,p_(F)= 70

A price floor is given along with demand and supply functions, where D(q) is the price, in dollars per unit, that consumers will pay for qunits, and S(q) is the price, in dollars per unit, at which producers will sell qunits. Find (a)the equilibrium point, ( (b) the point (q_(F),p_(F)) (c) the new consumer surplus, (d) the new producer surplus, and (e)the deadweight loss. D(q)=110-1.25q,S(q)=10+0.75q,p_(F)= 70
A price floor is given along with demand and supply functions, where D(q) is the price, in dollars per unit, that consumers will pay for qunits, and S(q) is the price, in dollars per unit, at which producers will sell qunits. Find (a)the equilibrium point, ( (b) the point (q_(F),p_(F)) (c) the new consumer surplus, (d) the new producer surplus, and (e)the deadweight loss. D(q)=110-1.25q,S(q)=10+0.75q,p_(F)= 70

Solution
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Answer

(a) Equilibrium point: (40, 60); (b) Point (q_{F}, p_{F}): (80, 70); (c) New consumer surplus: 1600; (d) New producer surplus: 0; (e) Deadweight loss: 400. Explanation 1. Find the equilibrium point Set D(q) = S(q) to find q. Solve 110 - 1.25q = 10 + 0.75q for q. This gives q = 40. Substitute q = 40 into either function to find p: p = 60. Equilibrium point is (40, 60). 2. Find the point (q_{F}, p_{F}) Given p_{F} = 70, substitute into S(q) to find q_{F}. Solve 70 = 10 + 0.75q for q. This gives q_{F} = 80. Point is (80, 70). 3. Calculate new consumer surplus Consumer surplus is area between demand curve and price floor from q = 0 to q_{F}. Use formula: \text{Consumer Surplus} = \frac{1}{2}(b-a)(h) where b = 110, a = 70, h = q_{F}. Calculate: \frac{1}{2}(110-70)(80) = 1600. 4. Calculate new producer surplus Producer surplus is area between supply curve and price floor from q = 0 to q_{F}. Use formula: \text{Producer Surplus} = \frac{1}{2}(h)(b-a) where b = 70, a = 10+0.75(80). Calculate: \frac{1}{2}(80)(70-70) = 0. 5. Calculate deadweight loss Deadweight loss is area between demand and supply curves from q_{F} to equilibrium quantity. Use formula: \text{Deadweight Loss} = \frac{1}{2}(b-a)(h) where b = 110-1.25(40), a = 10+0.75(40), h = 40. Calculate: \frac{1}{2}(60-40)(40) = 400.

Explanation

1. Find the equilibrium point<br /> Set $D(q) = S(q)$ to find $q$. Solve $110 - 1.25q = 10 + 0.75q$ for $q$. This gives $q = 40$. Substitute $q = 40$ into either function to find $p$: $p = 60$. Equilibrium point is $(40, 60)$.<br /><br />2. Find the point $(q_{F}, p_{F})$<br /> Given $p_{F} = 70$, substitute into $S(q)$ to find $q_{F}$. Solve $70 = 10 + 0.75q$ for $q$. This gives $q_{F} = 80$. Point is $(80, 70)$.<br /><br />3. Calculate new consumer surplus<br /> Consumer surplus is area between demand curve and price floor from $q = 0$ to $q_{F}$. Use formula: $\text{Consumer Surplus} = \frac{1}{2}(b-a)(h)$ where $b = 110$, $a = 70$, $h = q_{F}$. Calculate: $\frac{1}{2}(110-70)(80) = 1600$.<br /><br />4. Calculate new producer surplus<br /> Producer surplus is area between supply curve and price floor from $q = 0$ to $q_{F}$. Use formula: $\text{Producer Surplus} = \frac{1}{2}(h)(b-a)$ where $b = 70$, $a = 10+0.75(80)$. Calculate: $\frac{1}{2}(80)(70-70) = 0$.<br /><br />5. Calculate deadweight loss<br /> Deadweight loss is area between demand and supply curves from $q_{F}$ to equilibrium quantity. Use formula: $\text{Deadweight Loss} = \frac{1}{2}(b-a)(h)$ where $b = 110-1.25(40)$, $a = 10+0.75(40)$, $h = 40$. Calculate: $\frac{1}{2}(60-40)(40) = 400$.
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