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) b ² Area of triangle above P=80 + (80 - 30)(20) b ² Area of rectangle between P=80 and P=30 = 1200 PS = 1 2 (30 - 10)(20) = 200 (c) A price ±oor 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 speci²c 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 on average is the price Foor. However, there will be some consumers that are worse o± (because they don’t get the good). Best for producers on average is the price ceiling. However, there will be some producers that are worse o± (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:
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This note was uploaded on 04/26/2010 for the course ECON 101 taught by Professor Staff during the Spring '08 term at Vassar.

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

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