4 2 a under plan i the price is 2 per minute solving

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Exploring Microeconomics
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Chapter 12 / Exercise 4
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– 4 – 2.a. Under plan (i), the price is $2 per minute. Solving for Q: 2 = 11 - 0.1Q => Q = 90 minutes of calls per year. The annual cost (or total expenditure) under this plan would be TE = 2(90) = $180. Under plan (ii), there is a $129 flat charge for unlimited calls. In this case, the incremental price “P” is zero. In other words, P represents the opportunity cost of consuming another unit, given that you have already paid the $129 lump-sum fee. In this case, the opportunity cost of making another call is zero. Solving for Q: 0 = 11 - 0.1Q => Q = 110 minutes per year. The annual cost is $129. b. The customer chooses the plan that maximizes consumer surplus: CS(i)= 0.5(90)(11-2) = $405 (See Figure 1 below) CS(ii)= 0.5(110)(11) – 129 = $476 (See Figure 2 below: you cannot graphically depict consumer surplus, but you can indicate that it is the area of the shaded triangle below, which represents willingness to pay for 110 units, minus the up-front fee of $129.) Therefore, the customer should choose plan (ii).
90 110 Q P 11 2 Demand Plan (i) CS Figure 1 110 Q P 11 0 Demand Plan (ii) Figure 2
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Chapter 12 / Exercise 4
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– 5 – 3.(c)A decrease in the price of regular trucking services would shift the demand curve for package express services to the left. An increase in the price of package express services would move you upward, along the package express services demand curve. A decrease in the price of Internet goods that are shipped by package express companies would shift the package express service demand curve to the right. 4.The cross-price elasticity of demand for good Y with respect to the price of good X is: YX= %Qy/%Px. a. The cross-price elasticity between electricity and natural gas, commercial = 3.2 / 8 = 0.4; natural gas, residential = 6.4 / 8 = 0.8; electric power tools = -1/8 = -0.125. b. Electricity and natural gas are substitutes (positive cross-price elasticity), while electricity and electric power tools are complements (negative cross-price elasticity). 5.This question highlights that we draw inverse demand curvesin which Price is on the vertical axis, and Quantity is on the horizontal axis. The demand curves in this problem are written in the form Q = a - bP. The slope of this line is -b. The inverse demand curve is P = a/b - (1/b)Q, which has slope -1/b. Either representation of the line is fine; but you have to be clear about which you are using and you have to be consistent within a given problem. a.The slopes of the demand curves written as Q = a - bP are -1.0, -0.5 and -0.5, respectively. The slopes of the inverse demand curves are -1.0, -2.0, and -2.0, respectively. b.The own-price elasticity is defined as (Q/P)(P/Q) = -b(P/Q) where b is the slope of the demand curve (or 1/slope of the inverse demand curve). At P = 20, the elasticities are: (1) -1.0(20 / 180) = -0.11 (2) -0.5(20 / 90) = -0.11 (3) -0.5(20 / 190) = -0.053 c.No. The elasticity is defined in percentage terms, not in absolute terms. The elasticity is equal to the slope, adjusted by the base price and quantity (and also, 1/slope of the inverse demand curve, adjusted by the base price and quantity). You cannot directly infer the elasticity of demand from the slope of a linear demand curve without knowing where you are on that demand curve.

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