Exam I Answer Key. I. Definitions: Provide precise definitions for each of the following terms. (5 points each)

Transcription

1 Economics 10A Fall 1999 John F. Stewart Exam I Answer Key Instructions: Answer each question in the space provided. If you use graphs, make sure they are fully labeled. If a question asks for an explanation, one must be provided. Neatness and clarity of exposition count. You may use a calculator but no notes or books may be used. All provision of the Honor Code are in effect. I. (20 points) II. (30 points) III-1 (15 points) III-2. (20 points) III-3 (10 points) III-3. (5 points) Total (100 points) I. Definitions: Provide precise definitions for each of the following terms. (5 points each) 1. Inferior good A good for which the quantity purchased at a given price declines as the consumer income increases; a good with a negative income elasticity of demand. 2. Income elasticity of demand The percentage change in the quantity demand for a percent change in the consumers income, (holding price of the good and all other prices constant). % change in quantity demanded/% change in income 3. Law of diminishing marginal utility As the amount of one good consumed by a consumer increases (holding the consumption of all other goods constant) the marginal utility of the good will begin to get smaller and smaller. 4. Optimal purchase rule A consumer will maximize his utility by choosing to consume more of a good so long as the consumer s marginal utility exceeds the price the consumer must pay for the good. Choose optimal Q where P = MU Econ 10a, Exam 1, Page 1 of 5

2 II. Multiple Choice (5 points each) 2-1. If a consumer's demand curve for a product X is price inelastic (i.e. price elasticity is less than 1) then which of the following statements is true? a. An increases in the price of X will increase the consumer's total expenditure on the good X. b. An increase in the price of X will decrease the consumer's total expenditure on the good X. c. An increase in the price of X will leave the consumer's total expenditure on good X unchanged. d. The problem does not provide enough information to determine whether a price increase will change total expenditure on good X In the figure to the right the market demand curve for a good is shown by D and the supply curve by S. Given a price of $7.00, this market will a. be in equilibrium b. have a shortage of 4 c. have a shortage of 2 d. have a surplus of 4 e. have a surplus of Using the same diagram, the market equilibrium price and quantity would be a. P=7 Q=6 b. P=5 Q=10 c. P=3 Q=10 d. P=3 Q=6 e. P=5 Q=8 Figure for Questions 2-2, 2-3, and A perfectly competitive firm operating in the short run finds itself facing the following situation: The market price of the firms product is $1 per unit, the firm is currently producing 1000 units of the good and has a total fixed cost of $200 and a total variable cost of $1200. The short run marginal cost of producing 1000 units is $1. Given this information the firm should a. immediately stop all production and produce no output at all. Note: Though the firm has chosen the quantity where P = MC, average variable cost ($1200/1000=$1.20) is greater than price; the firm will loose less money if it shuts down. b. continue to produce 1000 units. c. expand its output until its marginal cost increases to $1 so it can cover more of its fixed cost. d. decrease its output a little so it can avoid some of its variable cost. e. None of the above, not enough information provided In the short run a farmer has 10 acres of land and is currently using 100 man hours of labor and 600 pounds of fertilizer. At the current level of input usage the marginal physical product of labor is 18 bushels of wheat per man hour and the marginal physical product of fertilizer is 5 bushels of wheat per pound of fertilizer. Assume that the price of fertilizer is $1 per pound and that the price of labor is $3 per man hour. Considering only the variable inputs (in the short run the quantity of land is fixed), is this farmer producing his current level of output at the least cost possible? a. Yes, he is using the proper mix of fertilizer and labor. b. No, he is using too much fertilizer and not enough labor. c. No, he is using too much labor and not enough fertilizer d. No, he is not producing at minimum cost, but there is not enough information provided to decide whether he should use more fertilizer or more labor. Econ 10a, Exam 1, Page 2 of 5

3 2-6. Explain your answer to question 2-5. At the farmers current choice of inputs one additional unit of output would cost $.20 if he bought enough fertilizer to produce one more unit of output ( P F /MPP F ). Doing the similar calculation for labor, it is costing him $.17 to produce the last unit of output using labor. Eliminating enough fertilizer to decrease output by 1 unit would save $.20; replacing that lost unit of output by buying enough labor would cost only $.17. The output would be the same but the total cost would be lower by $.03. III. Points as Shown 3-1. The table shows the marginal utility measured in dollar terms that a consumer gets from various levels of consumption. Cans of Coke Per Week Marginal Utility in $ s - $1.75 $1.25 $.95 $.85 $.40 $ $.25 a. (4 points) If the price of Coke is $.75 per can, the consumer will choose to consume 4 cans per week. Explain your answer: For each can 1 through 4 the marginal utility is greater than the cost (price) so net total utility increases. The fifth can would yield only $.40 of benefits so it is not worth the $.75 the consumer would have to pay to get it. b. (4 points) At the consumer's choice of consumption, how much consumer surplus will the consumer receive when the price is $.75 per can will be $ 1.80 (Surplus is total utility [ ] minus total cost (.75*4) c. (4 points) Coke decides that it will no longer sell Coke at $.75 per can, but rather it offers all the Coke you want for a fixed fee per week. If you accept Coke's deal, you pay a fixed amount and then you can have as many cans of Coke as you want per week, however, you cannot save Coke for the next week, nor can you give or sell Coke to anyone else. If you choose not to accept the deal, you get no Coke at all. -The LARGEST amount that the consumer shown in table would be willing to pay Coke for the "all you can drink deal" would be $5.25 per week - and the consumer would consume 6 cans per week. Explain your answer. All the consumer wants would be 6 cans. (Diminishing marginal utility holds, the MU of the 7 th can is negative) The most the consumer would agree to is a deal that yield 0 net total utility. Total utility of 6 cans is $1.75+$1.25+$.95+$.85+$.40+$.05=$5.25. d. (7 points) If Coke s average cost is $.50 per can and all consumers are identical to the one described in the table above, would it make sense for coke to offer the all you can drink plan? Explain. At a price of $.75 a piece cokes make a profit of $.25 a can and sells 4 cans to each consumer. The all you can drink plan results in an average revenue of $.875 per can or a $.375 profit per can and more cans are sold. Yes the all you can drink plan makes sense. It successfully converted consumer surplus into profits. If the consumer pays $.75 per can and buys 4, Coke s profits are $1.00. If Coke collects $5.25 form the consume and gives him 6 cans. Coke s profits are $2.25 Econ 10a, Exam 1, Page 3 of 5

4 3-2. The table below gives some of the values of the Total, Average and Marginal physical products for a firms production process when the capital (fixed input) is fixed at 3 units. Quantity of labor Total product of labor (Units of Output) Average physical product of labor Marginal physical product of labor a. In the table above, fill in the missing cells with the correct numerical values. (5 points) b. With the firm is in the short run and capital is fixed at 3 units, calculate the following cost information for the firm. Assume that the price of capital is $2.50 per unit and that the price of labor is $4 per unit. Show your work for each part. (8 points) - The total cost of producing 36 units of output = $19.50 Fixed cost are $2.50 x 3 = $7.50 variable cost are $4 x 3 = $12.00 Total cost is the sum - The average variable cost of producing 36 units of output = $.333 = TVC/Q = 12/36 - The average fixed cost of producing 36 units of output = $.208 = FC/Q = 7.5/36 - Your best approximation of the short run marginal cost of output at a current production level of 36 units? SRMC(36) = $.50 The easiest way is to remember the relationship between the product curves and cost SRMC = P input /MPP input = 4/8, Note that this is exactly the same thing as TC/ Q. b. Assume that the market price for the firms product is $.50 per unit and that the firm is a "price taking," profit maximizing firm in a perfectly competitive market. How many unit of output will the firm produce in the sort run (capital fixed at 3 units)? What will be the firm s short run profits? Carefully explain your answer. (7 points) Profit maximizing output (Q*) = 36 Firm would choose the output where P=MC if P>AVC. At 36 units of output MC=$.50 and P=$.50; AVC is $.333 so all conditions are met. Firm s profits = -$1.50 Total cost is $19.50 total revenue is $18.00 ($.50 x 36) so the firm has a loss (negative profits) of $1.50 Econ 10a, Exam 1, Page 4 of 5

5 3-3. Figure 2 shows the market demand and supply wooden toy trains. The market for wooden toy trains is perfectly competitive. Quantities are measured in number of trains per month. There are currently 1000 firms supplying the market. Also shown in the diagram are the average and $ MC $ $5 $3 $1 Figure 2 Typical Firm AC qfirm $5 $3 $1 Market Supply1000 Demand 1,000 10,000 15,000 20,000 50,000 marginal cost curves of a typical toy train firm. Assume that all firms in the market face identical cost conditions and that there are no fixed inputs in toy train manufacturing. (Thus there is no difference between long run and short run cost curves) a) Given that there are currently 1000 firms operating in the market, What will be the short run competitive equilibrium market price and quantity? Price $5, Quantity 15,000 b) How many trains is each of the 1000 firms producing a month? 15 c) How much profit will each firm be making at the equilibrium described in parts a). and b). Profits = slightly less than $30: total revenue = 15 x 5 = 75, AC is a little more than 3 so total cost is a little more than 45 d) In the long run, what do you expect to happen in this market? Why? Because there are profits, new firms will enter, this will shift the supply curve out and lower the market price. Process will continue until all profits have been dissipated. e) In the final long run market equilibrium, price (P) will be $3 and the market quantity (Q) will be 20,000 f) In the final long run equilibrium, there will be 2000 toy train firms each producing 10 trains per month (5 points) Using the demand curve shown in Figure 1 for problem 2-2., calculate the arc price elasticity of demand for a price change from 5 to 7. Show your work. Qmarket 0'& Q 1 & Q 0 (Q 1 % Q 0 )/2 P 1 & P 0 (P 1 % P 0 )/2 '& 8&6 (8%6)/2 5&7 (5%7)/2 '.857 Econ 10a, Exam 1, Page 5 of 5