ECONOMICS 1 - LECTURE 2 Suggested Answers to Problem Set #2

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1 Department of Economics Prof. Kenneth Train University of California, Berkeley Fall Semester 2011 ECONOMICS 1 - LECTURE 2 Suggested Answers to Problem Set #2 1. a) The data given in the problem tells us what the marginal willingnes to pay (MWTP) of Hiroo is. He will buy all the units for which the MWTP is higher than or equal to the price of a widget. (Note that he will buy a unit if his MWTP is equal to the price, since, by definition, MWTP is the maximum he s willing to pay, which means that he is willing to buy the good for that amount.) Since he is willing to pay $10 for the first widget he buys each year, and the price is $3, he'll buy it. He will also buy the second one, since he is willing to pay $9 for it and the price is still $3. And so on. Let's write the table for his MWTP to see how many he will buy: # of widgets MWTP W P W Consumer's Surplus From this table you can see that Hiroo will buy 8 widgets. That's when MWTP= P W. How do we know that he will stop buying at this point? What we have to do is to see if he is willing to buy the 9 th widget. Obviously he isn't, since he has to pay $3 to get it, but he is only willing to pay $2. Consumer's surplus is the difference between how much the consumer is willing to pay for a good and how much he/she has to pay (i.e. the market price) for each unit he/she

2 buys. This is what the fourth column in the table above shows. If Hiroo were to consume 1 unit, his consumer's surplus would be $7 ($10-$3); for 2 units, $7 from the first unit and $6 ($9-$3) from the second, $13 total; and so on. Since he is consuming 8 widgets, his total consumer's surplus is $28. b) When the price of a widget rises to $5, we have to change the last 2 columns of the table above. Hiroo's MWTP doesn't change when the price changes. # of widgets MWTP W P W Consumer's surplus From the table, and following the reasoning in part a), we can see that Hiroo is going to consume 6 units and his consumer's surplus will be $15. c) From the answers to parts a) and b), we can see that the consumer's surplus will decrease when the price of the commodity increases (and vice versa). In the graph below, we have Hiroo's demand curve for widgets. The area (A+B) represents his consumer's surplus when the price is $3 and area B is his consumer's surplus when the price is $5. Area A represents, therefore, the loss in consumer's surplus of an increase in the price of widgets from $3 to $5. 2

3 2. a) Average cost (AC) is equal to total cost (TC) divided by the number of units produced (q). Marginal cost (MC) is equal to the increase in total cost of producing one more unit. For instance, the marginal cost at 4 units is the extra cost of increasing production from 4 to 5 units, which is 62-59=3 dollars. q TC AC MC q TC AC MC b) The graphs will look like this: 3

4 c) Perfectly competitive market; market price = $18. i) The profit-maximizing output for your firm is 10 units. The firms expands production whenever MC<P. So the firm expands until it is selling 10 units (note: it expands from 9 to 10 because the MC at 9 is 17 which is less than the price) and then does not expand any further. ii) If you produced one more unit (increasing output to 11 units), your costs would rise by $23, but your revenue would rise by only $18. So your profits when producing 11 units would be lower by $5 than your profits when producing 10 units. If the firm decreases output from 10 to 9 units, its cost go down by 17 but its revenues go down by 18, such that it makes $1 less profit. iii) In order to calculate your profits you have to subtract your total costs from your total revenues. The price of a shirt is $18, so total revenues (price times quantity sold) are $180. Your total costs are $109. So: Total profits = total revenues - total costs = = $180 - $109 = $71. d) Since you are making positive economic profits, other firms will want to enter the market, shifting the supply curve of T-shirts to the right, lowering the market price below $18. e) If everyone who wanted to open a T-shirt shop did so, eventually (that is, in the long run) the price should go down to $10, which is the minimum average cost. This is the long-run equilibrium, because there'll be no incentives for new firms to enter the market. Why? The reason why new firms enter the market is that there are positive economic profits. But when the market price reaches $10, each firm will be producing (and selling) 8 T-shirts a week. Total costs are $80, and total revenues are $10 x 8 T-shirts = $80. And economic profits are $0. This means that there are no incentives for new firms to enter the market. f) One real-world factor that would prevent entry into the T-shirt market is the availability of space to open a shop. So not many firms could enter the market, the supply curve wouldn't shift by as much and the price wouldn't drop all the way to $10. That, of course, means that there would be excess demand for rental spaces and the rents should go up. But since there is rent control in Berkeley, that excess demand will remain unsatisfied, the rents won't go up, and neither will the costs. So the price will be lower than $18, but higher than $10 (which is the price at which economic profits are zero). The long-run equilibrium couldn't be achieved even though there would be positive economic profits because no more firms can enter the market. 4

5 3. The firm will expand output whenever P>MC. Price is 18 and MC is given by the formula MC=5q-30. So the firm will expand output whenever is 18>5q-30 48>5q 9.6>q. Since q is measured in thousands of units, this inequality means that the firm will expand whenever its output is below 9,600. So when its output is 9,599, it will expand to 9,600. At 9,600, output is no longer below 9,600, and so it does not expand any more. It stays at 9,600. At this output, MC=5(9.6)-30=18 such that P=MC. This example shows why we say the firm chooses output where P=MC rather than using the longer statement the firm expands output whenever P>MC --- because output is usually large enough such that fractional units are not a relevant issue and the two statements become the same. 4. To answer to this question, you have to use the word "competitive" in the sense of a firm acting in perfect competition as you saw in lecture. It's different from the everyday use of the word, in that firms are not competing each other (e.g. setting a lower price to attract more customers) since they can only adjust their output, given the market price. The case of the retail food industry (supermarkets) is not a case of perfect competition, that is, the firms are not competitive in the economics sense of the word. Why? Let's follow the order in which the questions were presented in the problem set: a)-b) In order for a market to be competitive, it needs to have many firms that are small compared to the market. How many firms are there in the retail food industry and how big are they? You have 2 big firms (Lucky and Safeway), and probably a third (Andronico's), which cover a large portion of the market. There are also some small firms (small food stores in which you occasionally buy something, but where you most likely don't do your weekly shopping). But there is also the fact that they are not the same (at least not to consumers). As long as you can make a distinction between firms, you are not in perfect competition. Remember what Prof. Train said in lecture: in perfect competition, goods have to be identical, or at least have to be considered identical by consumers. Which leads us to the next part. c) Obviously you can get different prices in different places. If you have ever gone to Andronico's, you know that it's more expensive than buying from Lucky or Safeway. And this can be possible because of the fact that firms are not the same. They have names that consumers distinguish and some prefer to buy in one particular place than in other, even though the price is higher. d) Regarding costs, big firms seem to have same costs. They usually buy from the same food suppliers, except for their own brands. And they are getting their labor force from the same pool of workers. But that's not the case for small firms, which have to pay a higher price due to the small amounts they buy. e) Entry to the industry in fairly free for small shops, which are not going to "compete" with the big firms. But large firms would have a hard time establishing name recognition and relations with suppliers like existing firms have. 5

6 f) Profits are not high for food stores; in fact they seem to be fairly low. So prices are probably close to average cost. Also, there are periodic price wars, which keep prices and profits low. g) Overall, the industry does not match our conditions for competition very closely. There are a few large firms among the numerous small ones, and entre is not really free, at least for large firms. However, the outcome nevertheless seems to be pretty close to the outcome we would expect from a competitive industry: prices close to cost and low profit. So this is an example of how the benefits of competition can sometimes come about even when the conditions for competition are fully me 5. a. The monopolist chooses where MR=MC. The output at which MR=MC is The highest price the monopolist can charge and sell this output is $9. Therefore the monopolist sets price at $9 and produces and sells 6000 units. Its marginal revenue is $6 when it is producing 6000 units. b. Price equals marginal cost where the demand curve and MC curve intersect, which is at a price of $8 and quantity of Stated alternatively: When price is set at $8, the quantity demanded is 8000; and when 8000 units are being produced, the marginal cost of an additional unit is $8, such that price equals marginal cost. c. i) The gain in consumer surplus is (9-8)x (9-8)x( )/2 = =7000. ii) At a price of $9, total revenues are 9x6000=54,000. At the price of $8, total revenues are $8x8000=64,000. So revenues go up by $10,000. Now consider costs. Costs increase by 6x( ) + (8-6)x( )/2 = 12, = 14,000. Since revenues rise by $10,000 and costs rise by $14,000, profits drop by $4,000. Note that the $7000 gain to consumers is greater than the $4000 recution in profits for the firm, such that moving from the monopolist's chosen price to the socially optimal price results in a net benefit to society of $