Introduction to Industrial Organization, 2nd Ed Solutions to End-of-Chapter Exercises

Introduction to Industrial Organization, 2nd Ed Solutions to End-of-Chapter Exercises Lu´ıs Cabral This draft: March 2017 Please address questions or corrections to 1 Introduction 1.1. Competition and performance.Empirical evidence from a sample of more than 600 UK firms indicates that, controlling for the quantity of inputs (that is, taking into account the quantity of inputs), firm output is increasing in the number of competitors and decreasing in market share and industry concentration.1 How do these results relate to the ideas presented in this chapter? Answer: In Section 1.2, I argued that one of the implications of market power is the decline of productive efficiency. Controlling for input levels, the level of output is a measure of productive efficiency. The number of competitors and the degree of concentration are measures of the degree of competition (concentration is an inverse indicator). The empirical evidence from UK firms is therefore consistent with the view presented in the text. 2 Consumers 2.1. Fruit salad. Adam and Barbara are big fruit salad fans (and both agree that the more the better). However, their tastes differ regarding the way the salad is made. For Adam, for each apple you throw in, there should be one and only one banana (if you give him more than one banana, he will throw it way). For Barbara, as long at it’s fruit, it doesn’t matter; in other words, all that counts is the number of pieces of fruit. (a) Show what Adam’s and Barbara’s indifference curves look like. Answer: Figure 2.1 depicts Adam’s and Barbara’s indifference curves (left and right panels, respectively). (b) Are apples and bananas substitutes or complements? Answer: For Adam, apples and bananas are perfect complements; for Barbara, perfect substitutes. 2.2. Village microbrew. Village microbrew raised its price from $10 to $12 a case (wholesale). As a result, sales dropped from 10,500 to 8,100 (in units). Based on your estimate of the demand elasticity, what percent change in sales would you predict if price were cut from $10 to $9? What demand level would this correspond to? Figure 2.1 Indifference curves: Adam and Barbara bananas bananas 3 3 2 2 1 1 1 2 3 apples 1 2 3 apples Answer: We can approximate it by the “change formula,” ϵ ≈ ∆ q p = 10, 500 − 8, 100 12 = −1.77 ∆ p q 10 − 12 8, 100 This is approximate, since we’re using discrete changes. If we assume that the elasticity of demand is constant then we could get an exact solution by using the log formula: ϵ = ∆ log q = log 10500 − log 8100 = −1.42 ∆ log p log 10 − log 12 Did revenue rise or fall? Since ϵ −1, the increase in prices led to an overall fall in revenue. (If you want to make sure, then calculate the revenues before and after the price change.) If the elasticity is constant, what is the demand at $9? If the elasticity is constant then the log formula calculates the elasticity exactly and in addition we know that: log 10500 − log q9 = 1.42 log 10 − log 9 where q9 is the demand when the price is $9 per case, so (after a little bit of algebraic manipulation) q = exp log 10500 + 1.42 log 10 = 12195 With constant demand elasticity, the percent variation method only gives an approximation of the value of demand elasticity. Moreover, estimating demand for a different price level will give a different value than the log formula. Specifically, the demand estimate when price is $9 is given by q9 = 10500 1 + (−1.77) × (−10%) = 12358 since the drop in price from 10 to 9 corresponds to a −10% variation 2.3. Demand elasticity. Based on the values in Table 3.2, provide an estimate of the impact on sales revenues of a 10% increase in each product’s price. Answer: Revenue is given by R = p × q. Differentiating, we get dR = dp q + p dq Dividing by R, dR q = dp R R p + dq R Since R = p q and ϵ = dq/dp p/q, we have dR q = dp R R p + dq R q = dp + p q dp dp = + p p dp dp = + p p p dq p q p dq q dp ϵ = dp 1 + ϵ Given that d p/p = 10%, we have Product dR/R Milk (1 − 0.5) × 10% = 5% Cigarettes 5% Beer 2% Apples -3% US luxury cars in US -9% Foreign luxury cars in US -18% 2.4. Smartphones. The following pairs of price and quantity demanded for smartphones have been observed: (100, 600); (105, 590); (110, 575); (115, 550); and (120, 510). (a) Calculate the approximate elasticity of demand when price is $105. Answer: Using the percent variation method, an increase in price to 110 leads to an estimate of elasticity of (575 − 590)/(110 − 105)105/590 = −.53. A decrease in price to 100 leads to an estimate of elasticity of (600 − 590)/(100 − 105)105/590 = −.36. We conclude that the value of the demand elasticity is somewhere between −.36 and −.53. Alternatively, we can approach this problem by using logs. The elasticity estimates would then be (log(575) − log(590))/(log(110) − log(105)) = −.55 for a price increase and (log(600) − log(590))/(log(100) − log(105)) = −.34 for a price decrease. (Notice that, while the estimates at each point are quite different, the resulting range is similar.) (b) Is the demand elasticity constant at all prices? Answer: Generally speaking, the value of demand elasticity does not need to be constant at all price levels. In this particular case, it can be shown that it is not. In fact, if the demand elasticity is constant, then the estimate obtained by using the log formula gives the exact value of elasticity. As shown in part (a), the estimates obtained with the logs formula applied to two different pairs of points are different. It follows that the value of ϵ varies for different price levels. This is consistent with the rather wide range of estimates we obtained in the previous question. (c) How does the value of demand elasticity vary as price increases? Answer: Using logs and computing the elasticity at each point based on a $5 price increase, we obtain the following estimates, starting at $100 : −.35, −.55, −1.00, −1.77. This pattern is not infrequent: as we increase price, demand elasticity increases (in absolute value). (d) If the monthly subscription fee for Internet access from a cell phone falls from $10 to $2, what would you expect to happen to the quantity of cell phones demanded at any given price? What effect would this Internet access price change have on the mobile phones’ elasticity of demand? Answer: We would expect the quantity of phones demanded to increase at all price levels when the price of Internet access, a complementary product, decreases. However, it would be difficult to determine what the change in demand elasticity would be at any given price point. 2.5. Cars. Table 2.2 gives the “own” and cross-price elasticities for selected automobile models.2 Specifically, each cell corresponds to the demand elasticity of the car model listed in the row with respect to changes in the price of the car model listed in column. (a) Why are the “own” elasticities so high? Answer: These are models for which many substitute models are available. Thus, even if the demand for cars is not very elastic, the demand for a particular model is. (b) Are the Accord and Taurus complements or substitutes? Answer: The cross-price elasticity of the Accord with respect to the price of the Taurus is given by 0.1, a positive value. The two models are therefore substitutes. In fact, no two models in this sample are complements. (c) What are the Taurus’s closest competitors? Answer: Looking at the Taurus row, we see that the cross-price elasticity is highest for the Accord. In other words, a 1% change in the price of the Accord would have a greater impact on the demand for the Taurus, than a 1% change in the price of any other model (other than the Taurus). (d) If GM lowers the price of its Chevy Cavalier, does it “cannibalize” its Buick Century sales? Answer: Yes. However, the cross price elasticity of the Century with respect to the price of the Cavalier is fairly small. Therefore, a decrease in the price of the Cavalier will reduce the demand for the Century by only a small amount. (e) Why is the direct elasticity for the Mazda not lower than the elasticity for more expensive models (as the rule of thumb would sug- gest)? Answer: As suggested by the qualitative analysis of demand elasticity, luxuries tend to have higher elasticity than non-luxuries. However, another rule of thumb to keep in mind is that the elasticity for a particular product is always higher than the elasticity for the group of products it belongs to. As it happens, there are many more compact car models than there are luxury car models. Therefore, even though the elasticity for luxury cars is higher than the elasticity for compact cars, the elasticity for a particular luxury model may not be much greater than the elasticity for a particular compact car. (f) Suppose Honda sold 300k Accords in 2001. In 2002, the price of the Accord decreased by 2%, whereas the price of the Taurus de- creased by 3%. What is the likely change in Accord sales? Answer: The percent change in demand is approximately given by (−2%) × (−4.8) + (−3%) × (0.1) = 9.3%. We would expect an increase in Accord sales of approximately 9.3%, or .093 × 300k = 27.9 k units. 2.6. Netflix and Hulu. Suppose the demand for Netflix is given by qN = a − bN pN + bB pB where qN is the number of Netflix subscriptions, pN the price of a Netflix plan, and pH the price of a Hulu plan. (a) What is the price elasticity of Netflix subscriptions? Answer: The price elasticity is ϵ = d qN d pN pN = b pN qN qN Note the demand is elastic for high values of pN/qN and inelastic for low values of pN/qN. (b) Suppose a = 500, bN = 10, bH = 5, and pH = pN = 50. What are N ’s elasticity and cross-price elasticity? Are products N and H substitutes or complements? Answer: The cross-elasticity of Netflix with respect to Hulu’s price is given by ϵNH = d qN d pH pH = b pH qN qN Substituting the values in the above expressions, we get ϵ = −2, and ϵNH = 1. The positive sign of the cross-elasticity means the products are substitutes. (You might have guessed it.) (c) How much do consumers get in surplus at these prices? Answer: Consumer surplus is the area under the demand curve but above the price. First we compute the choke price, that is the highest value of willingness to pay. Since qN = a − bN pN + bH pH when a = 500, bN = 10, bH = 5, and pH = pN = 50 we get qN = 500 − 10 pN + 5 × 50 If qN = 0, then pN = (500 + 250)/10 = 75. This means the choke price is given by 75. Next we compute total output at the prevailing prices. This is given by qN = 500 − 10 × 50 + 5 × 50 = 250 Since demand and cost are linear, consumer surplus is a triangle where the height is the difference between the demand choke price (75) and price (50), whereas the base is output (250). This implies 1 CS = 2 × 250 × (75 − 50) = 3125 2.7. Lamborghini. The current US demand for the Lamborghini Gallardo SE is elastic; specifically, it is estimated that demand elasticity is given by ϵ = −3. The current price is p = $120k. Annual sales at this price amount to q = 160 (number of cars). (a) What do you estimate would be the impact of an increase in price to $140k?