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ps3f06s - Economics 101 Problem Set 3 Solutions Alan C...

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Economics 101, Problem Set 3 Solutions Alan C. Marco 1. Suppose market demand is given by P =100 - Q and supply is given by P =10+ Q. For each situation, solve for the equilibrium, consumer surplus, and producer surplus. (a) The free market equilibrium. P * =55 ,Q * =45 CS = 1 2 (100 - 55)(45) = 1012 . 5 PS = 1 2 (55 - 10)(45) = 1012 . 5 (b) A price ceiling is imposed at P =30 . P =30 ,Q D =70 ,Q S =20 (binding). CS = 1 2 (100 - 80)(20) bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright Area of triangle above P=80 + (80 - 30)(20) bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright Area of rectangle between P=80 and P=30 = 1200 PS = 1 2 (30 - 10)(20) = 200 (c) A price floor is imposed at P =60 . P =60 ,Q S =50 ,Q D =40 (binding). CS = 1 2 (100 - 60)(40) = 800 PS = 1 2 (50 - 10)(40)+(60 - 50)(40) = 1200 (d) A $10 per unit tax is imposed on suppliers. [Be specific about the retail price, price to consumers and suppliers, and quantity.] 100 - Q = 10+ Q +10 Q * = 40 P cons = 60= P retail P prod = 50 CS = 1 2 (100 - 60)(40) = 800 PS = 1 2 (50 - 10)(40) = 800 1
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(e) Which outcome is best for consumers? Producers? Best for consumers onaverage is the price floor. However, there will be some consumers that are worse off (because they don’t get the good). Best for producers onaverage is the price ceiling. However, there will be some producers that are worse off (because they aren’t able to sell the good). 2. Show graphically when the following policies will lead to the (i) lowest and (ii) highest deadweight loss; i.e., with inelastic or elastic demand, inelastic or elastic supply? [Assume that long-run elasticity is the same as short-run for the purposes of the exercise.] (a) rent-control 1. Lowest: inelastic supply, elastic demand. 2. Highest: elastic supply, inelastic demand. (b) an excise (per unit) tax 1. Lowest: inelastic supply and demand. 2. Highest: elastic supply and demand. (c) minimum wage 1. Lowest: elastic supply, inelastic demand. 2. Highest: inelastic supply, elastic demand. 3. Suppose market demand is given by P =100 - Q and supply is given by P =10+ Q. (a) What is the free market equilibrium? Solving the two equations gives 100 - Q = 10+ Q Q * = 45 P * = 55 (b) What is the outcome if a price ceiling is imposed at P =30? Quantity demanded: 30 = 100 - Q D Q * D = 70 Quantity supplied: 30 = 10+ Q S Q * S = 20 Q =20 is actually traded at P =30 , leaving a shortage of 50.
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