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Chap 12 13

# Chap 12 13 - Chapter 12 13 Solutions Problem ST12.2 The...

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Chapter 12 & 13 Solutions

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Problem ST12.2 The market supply curve is given by the equation Q S = 10P or, solving for price, P = 0.1Q S The market demand curve is given by the equation Q D = 120 - 40P or, solving for price, 40P =120 - Q D P = \$3 - \$0.025Q D
Problem ST12.2 To find the competitive market equilibrium price, equate the market demand and market supply curves where quantity is expressed as a function of price: Supply = Demand 10P = 120 - 40P 50P = 120 P = \$2.40 To find the competitive market equilibrium quantity, set equal the market supply and market demand curves where price is expressed as a function of quantity, and Q S = Q D : Supply = Demand \$0.1Q = \$3 - \$0.025Q 0.125Q = 3 Q = 24 (million) units per month

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Problem ST12.2 Therefore, the competitive market equilibrium price-output combination is a market price of \$2.40 with an equilibrium output of 24 (million) units. The value of consumer surplus is equal to the region under the market demand curve that lies above the market equilibrium price of \$2.40. Because the area of such a triangle is one-half the value of the base times the height, the value of consumer surplus equals: Consumer Surplus = ½ [24 ×(\$3 - \$2.40)] = \$7.2 (million) per month In words, this means that at a unit price of \$2.40, the quantity demanded is 24 (million), resulting in total revenues of \$57.6 (million). The fact that consumer surplus equals \$7.2 (million) means that customers as a group would have been willing to pay an additional \$7.2 (million) for this level of market output. This is an amount above and beyond the \$57.6 (million) paid. Customers received a real bargain. The value of producer surplus is equal to the region above the market supply curve at the market equilibrium price of \$2.40. Because the area of such a triangle is one-half the value of the base times the height, the value of producer surplus equals: Producer Surplus = ½ [24 ×(\$2.40 - \$0)] = \$28.8 (million) per month
Problem ST12.2 At a water price of \$2.40 per thousand gallons, producer surplus equals \$28.8 (million). Producers as a group received \$28.8 (million) more than the absolute minimum required for them to produce the market equilibrium output of 24 (million) units of output. Producers received a real bargain. In competitive market equilibrium, social welfare is measured by the sum of net benefits derived by consumers and producers. Social welfare is the sum of consumer surplus and producer surplus: Social Welfare = Consumer Surplus + Producer Surplus = \$7.2 (million) + \$28.8 (million) = \$36 (million) per month

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Problem ST12.2 Las Vegas Valley Water District \$0.00 \$0.50 \$1.00 \$1.50 \$2.00 \$2.50 \$3.00 \$3.50 0 4 8 12 16 20 24 28 32 36 40 Quantity (000) Price MC = \$0.1Q Demand P = \$3 - \$0.025Q D C B A Monopoly Deadweight Loss MR = \$3 - \$0.05Q 0 Consumer Surplus Transferred to Producer Surplus
Problem ST12.2 If the industry is run by a profit-maximizing monopolist, the optimal price-output combination can be determined by setting marginal revenue equal to marginal cost and solving for Q : MR = MC = Market Supply \$3 - \$0.05Q = \$0.1Q \$0.15Q = \$3 Q = 20 (million) units per month At Q = 20, P = \$3 - \$0.025Q = \$3 - \$0.025(20) = \$2.50 per unit

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Problem ST12.2 Under monopoly, the amount supplied falls to 20 (million) units and the market price jumps to \$2.50 per thousand gallons of water. The amount of deadweight loss from monopoly suffered by consumers is given by the triangle bounded by ABD in the figure.
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