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ECON 102 Tutorial: Week 4 Ayesha Ali www.lancaster.ac.uk/postgrad/alia10/econ102.html [email protected] office hours: 8:00AM – 8:50AM tuesdays LUMS C85 Maths & Stats Help The LUMS Maths and Stats Help (MASH) Centre for LUMS undergraduate students opens this week. You can drop-in to LUMS B38a every Monday (16.00-18.00) and Friday (10.00-12.00) Or, book an appointment to see a student mentor and get help with maths and stats. Book by going to the LUMS Effective Learning Moodle site or directly to TARGETconnect. Email [email protected] with any queries. Question 1: Ch 4 Question 8 Using indifference curves, show how a price rise for one good affects consumption of that good by: a) Lowering the consumer’s real income, and b) Altering relative prices of the two goods. Using Indifference Curves to show Income and Substitution Effects In a two-good model of consumption, when a price change occurs, we will have two effects on our consumption: a substitution effect and an income effect: How do we graph this? First, we draw our original budget constraint, original indifference curve, and the new budget constraint which comes from the change in price of one good. Next, we can find the substitution effect, the movement along the indifference curve, to a point whose MRS is equal to the slope of the new budget constraint. Finally, we can find the income effect – which will move us to a new indifference curve on the new budget constraint. Where we move due to the income effect depends on whether our good whose price changed is a normal, inferior or giffen good. For a detailed explanation of how to use indifference curves to show income and substitution effects in response to a price change this video is very thorough. Another Example: We have two goods, pizza and Pepsi. Pizza is on the x-axis and Pepsi is on the y-axis. Show what happens when the price of Pepsi decreases if Pepsi is a normal good. Question 1: Ch 4 Question 8 Here is Prof. Rietzke’s solution; basically it gives the same explanation as we did in class: A price rise in one good means that less of it can be bought given a fixed budget. Hence, the budget constraint swivels around the intercept point of the other good. In reference to Figure 4.17 in the textbook, we can demonstrate that if good B has become more expensive the budget constraint becomes steeper, hence the intercept for good B moves closer to the origin (no change to the price of good A). Two things happen: 1) there is an income effect, which means that the consumer is moved to a lower indifference curve (the consumer’s purchasing power is reduced, and hence can no longer attain the original indifference curve); and 2) The substitution effect kicks in as the relative prices of goods A and B have changed. Good A now is a better bargain and there is a substitution towards the now cheaper good. In Figure 4.17, start at point 1, the original bundle before the price change. Now good B becomes more expensive and the budget constraint becomes steeper. If we could compensate the consumer for the loss in income, then this consumer could remain on the old indifference curve, and would only have to consider the change in relative prices (i.e. we strip out the income effect with this trick and concentrate on the substitution effect only). Graphically this is shown by a parallel shift of the new budget constraint until it just touches the old indifference curve (shown by the orange budget constraint in Figure 4.17). Consumption would be at point 3. The move from point 1 to 3 shows the substitution effect only. Hence, the move from point 3 to point 2, the new bundle after the price change, shows the income effect only. Question 1: Ch 4 Problem 6(a) Anna Lucia lives in Cremona and commutes by train each day to her job in Milan (20 round trips per month). When the price of a round trip goes up from €10 to €20, she responds by consuming exactly the same number of trips as before, while spending €200 per month less on restaurant meals. Does the fact that her quantity of train travel is completely unresponsive to the price increase imply that Anna Lucia is not a rational consumer? The concept of consumer rationality states that a consumer will allocate his or her budget between goods so that the ratio of marginal utility to price is the same across all goods (that’s the rational spending rule from last week). So, even at twice the original price, the marginal utility per euro of the 20th train trip may be higher than the corresponding ratio for any other good that Anna Lucia might consume, in which case she would be perfectly rational not to alter the number of trips she takes. After all, missing a trip would be to miss a whole day’s work. Question 1: Ch 4 Problem 6(b) Explain why an increase in train travel might affect the amount she spends on restaurant meals. The higher price of train tickets makes Anna Lucia poorer. The income effect of the price increase is what leads to the reduction in the number of restaurant meals she eats. Question 2(a) Karen divides her budget between two goods: good one and good two. Using indifference curve analysis, graphically illustrate the effect on consumption of both goods if the price of good one decreases; goods one and two are substitutes. (for each part of this question, put good two on the y-axis and good one on the x-axis) Question 2(a) Karen divides her budget between two goods: good one and good two. Using indifference curve analysis, graphically illustrate the effect on consumption of both goods if the price of good one decreases; goods one and two are substitutes. (for each part of this question, put good two on the y-axis and good one on the x-axis) Before the price decrease, the optimal bundle is at the point A. When the price of good one decreases, the budget line shifts out from B1 in red to B2 in green. After the price decrease, the optimal bundle is at the point B. Because goods 1 and 2 are substitutes, when the price of good 1 decreases, the consumer consumes less good 2. So, at the new optimal bundle, the consumer consumes more good 1 and less good 2. Question 2(b) Karen divides her budget between two goods: good one and good two. Using indifference curve analysis, graphically illustrate the effect on consumption of both goods if the price of good one increases; goods one and two are complements. (for each part of this question, put good two on the y-axis and good one on the x-axis) Question 2(b) Karen divides her budget between two goods: good one and good two. Using indifference curve analysis, graphically illustrate the effect on consumption of both goods if the price of good one increases; goods one and two are complements. (for each part of this question, put good two on the y-axis and good one on the x-axis) Before the price decrease, the optimal bundle is at the point A. When the price of good one increases, the budget line shifts inwards from B1 in red to B2 in green. After the price increase, the optimal bundle is at the point B. Because goods 1 and 2 are complements, when the price of good 1 increases, the consumer consumes less good 2. So, at the new optimal bundle, the consumer consumes less good 1 and less good 2. Question 2(c) Karen divides her budget between two goods: good one and good two. Using indifference curve analysis, graphically illustrate the effect on consumption of both goods if Karen’s income increases; goods one and two are normal. (for each part of this question, put good two on the y-axis and good one on the x-axis) Question 2(c) Karen divides her budget between two goods: good one and good two. Using indifference curve analysis, graphically illustrate the effect on consumption of both goods if Karen’s income increases; goods one and two are normal. (for each part of this question, put good two on the y-axis and good one on the x-axis) When Karen’s income increases, her budget line shifts outwards from B1 in red to B2 in green. Her optimal bundle moves from point A to point B. Since both goods are normal, her consumption of both goods increases following the increase in her income Question 2(d) Karen divides her budget between two goods: good one and good two. Using indifference curve analysis, graphically illustrate the effect on consumption of both goods if Karen’s income decreases; good one is normal and good two is inferior. (for each part of this question, put good two on the y-axis and good one on the x-axis) Question 2(d) Karen divides her budget between two goods: good one and good two. Using indifference curve analysis, graphically illustrate the effect on consumption of both goods if Karen’s income decreases; good one is normal and good two is inferior. (for each part of this question, put good two on the y-axis and good one on the x-axis) When Karen’s income decreases, her budget line shifts inwards from B1 in red to B2 in green. Her optimal bundle moves from point A to point B. Because good 1 is normal, Karen decreases her consumption of good 1. And because good 2 is inferior, a decrease in her income leads her to consume more of good 2. Question 3: Ch. 5 Problem 1(a) Zoe is trying to decide how to divide her time between her job as a wedding photographer, which pays €27 per hour for as many hours as she chooses to work, and as a fossil collector, in which her pay depends both on the price of fossils and the number of them she finds. Earnings aside, Zoe is indifferent between the two tasks, and the number of fossils she can find depends on the number of hours a day she searches, as shown in the table below. Hours per day Total fossils per day (1) (2) 1 5 2 9 3 12 4 14 5 15 Derive a table with price in euro increments from €0 to €30 in column (1) and the quantity of fossils Zoe is willing to supply per day at that price in column (2). Question 3: Ch. 5 Problem 1(a) Derive a table with price in euro increments from €0 to €30 in column (1) and the quantity of fossils Zoe is willing to supply per day at that price in column (2). 1. If the price of a fossil is less than €6, Zoe should devote all her time to photography because when the price is, say, €5 per fossil, an hour spent looking for fossils will give her 5(€5) = €25, or €2 less than she’d earn doing photography. If the price of fossils is 6, Zoe should spend one hour searching, will supply 5 fossils, and will get €30 revenue, which is €3 more than she’d earn from photography. However, an additional hour would yield only 4 additional fossils or €24 additional revenue, so she should not spend any further time looking for fossils. If the price of fossils rises to €7, however, the additional hour gathering fossils would yield an additional €28, so gathering fossils during that hour would then be the best choice, and Zoe would therefore supply 9 fossils per day. Using this reasoning, we can derive a price-quantity supplied relationship for fossils as follows: Price of fossils (€) 0-5 6 7, 8 9-13 14-26 27+ Hours per day Total fossils per day (1) (2) 1 5 2 9 3 12 4 14 5 15 Number of fossils supplied per day 0 5 9 12 14 15 Question 3: Ch. 5 Problem 1(b) Using the table you found in part (a), plot these points in a graph with price on the vertical axis and quantity per day on the horizontal. What is this curve called? If we plot these points, we get Zoe’s daily supply curve for fossils: Price of fossils (€) 0-5 6 7, 8 9-13 14-26 27+ Number of fossils supplied per day 0 5 9 12 14 15 Question 4(a) The table below gives the relationship between the number of workers in a firm, and the total output that can be produced per day. Workers are paid $20 per day. Fill in the rest of the table, expressing each of the costs in the cost per day for the firm. (Note: AFC is average fixed cost, AVC is average variable cost, ATC is average total cost, and MC is marginal cost) Average fixed cost: Average variable cost: Average total cost: AFC = FC/Q AVC = VC/Q ATC = TC/Q Marginal cost per unit of output: MC = Workers Q 0 0 1 25 2 63 3 94 4 119 5 140 6 158 Fixed Costs ∆ ∆ Variable Costs Total Cost AFC AVC ATC MC 10 - - - - Question 4(a) The table below gives the relationship between the number of workers in a firm, and the total output that can be produced per day. Workers are paid $20 per day. Fill in the rest of the table, expressing each of the costs in the cost per day for the firm. Average fixed cost: AFC = FC/Q Average variable cost: AVC = VC/Q Average total cost: ATC = TC/Q Marginal cost per unit of output: Workers Q Fixed Costs 0 0 10 1 25 2 MC = ∆ ∆ Variable Costs Total Cost AFC AVC ATC MC 0 10 - - - - 10 20 30 0.400 0.800 1.200 0.800 63 10 40 50 0.159 0.635 0.794 0.526 3 94 10 60 70 0.106 0.638 0.745 0.645 4 119 10 80 90 0.084 0.672 0.756 0.800 5 140 10 100 110 0.071 0.714 0.786 0.952 6 158 10 120 130 0.063 0.759 0.823 1.111 Question 4(b) Graph the firm’s ATC, AVC, and MC curves. 1.400 $ 1.200 1.000 0.800 AVC ATC MC - 0.600 0.400 0.200 0.000 1 2 3 4 5 6 No. of workers - Question 4(c) Does this production technology exhibit diminishing marginal products? Explain. From our table, we know the second worker produces an additional 38 units, which is more than the first worker produces. After the second worker, each additional worker produces less additional output than the previous worker. Therefore, for W > 2 (where W is the number of workers) the production technology does exhibit decreasing marginal products. For W ≤ 2, the production technology exhibits increasing marginal products. Next Week Multiple Choice Exam in Week 6 on Friday 20 questions from Prof. Rietzke (economics questions) Covering material up until the Tutorial 6 worksheet 10 questions from Prof. Peel (maths questions) Exactly like his maths practice questions at the end of lecture notes. Check your timetable for exam time and location. Study & Review lecture slides, tutorial questions, and maths questions.