eco204_HW_2_solution - 1 ECO 204 2008‐2009 Ajaz Hussain...

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Unformatted text preview: 1 ECO 204 2008‐2009 Ajaz Hussain HW 2 Solutions Question 1 (Based on HW1 & 2007‐2008 Final Exam Question) In a marketing survey, customers were asked about their preferences over cigarettes and coffee. The results indicate that customers perceive cigarettes and coffee to be pleasurable (‘good’ goods) and have increasing marginal rate of substitution. (a) Will consumers engage in “addictive” behavior? If so, when will they consume coffee only? Answer: Yes, it is possible. Suppose cigarette and coffee prices are uniform (i.e. do not vary by volume), then‐‐ as we saw in lecture 2‐‐ it is possible to consume just cigarettes or just coffee (“addictive behavior”) as depicted in Figures 1 and 2. (In these figures, I have deliberately drawn the budget line so that it gives only one corner solution. You should draw a case where the budget line can give two possible corner solutions and then attempt the questions below with this model). The addict will consume cigarettes only if the ratio of coffee to cigarette prices is high. Similarly, the addict will consume coffee only if the ratio of coffee to cigarette prices is low. You should convince yourself of this by checking when the budget line below is steep and flat. ECO 204, 2008‐2009. Ajaz Hussain. Department of Economics, University of Toronto 2 Figure 1 Figure 2 (b) In part (a), what happens to coffee consumption as the price of coffee decreases? Answer: As the price of coffee decreases, the budget line become flatter since its slope ‐ P1/P2 = ‐Pcoffee /Pcigarettes falls. At the same time, the budget line swings out, since the x‐ axis intercept Y/P1 = Y/Pcoffee becomes larger. ECO 204, 2008‐2009. Ajaz Hussain. Department of Economics, University of Toronto 3 What happens to coffee consumption depends on the initial situation. Suppose the consumer is already addicted cigarettes (Figure 1 above) so that the consumer is drinking zero cups of coffee. As the price of coffee falls, initially there is no change in quantities of coffee consumed. But as the price drops low enough, there will come a point where the consumer switches from cigarettes to coffee as shown in Figure 3: Figure 3 Thus, the demand curve for coffee will look like (the downward sloping part is for illustrative purposes: for example, the downward sloping part could be linear) as depicted in Figure 4. One of the implications here is that for some ranges of coffee prices the price elasticity of coffee (% change in coffee consumption/ % change in coffee prices) is zero. An analyst, working in this range of prices may conclude that coffee sales do not respond to coffee prices. This, as you can see, is not a global statement. ECO 204, 2008‐2009. Ajaz Hussain. Department of Economics, University of Toronto 4 Figure 4 On the other hand, suppose the consumer was already a coffee addict: in that case, the demand curve will be (assuming that consumer was a coffee addict from price of $0 on): Figure 5 ECO 204, 2008‐2009. Ajaz Hussain. Department of Economics, University of Toronto 5 (c) In part (a), what happens to cigarettes consumption as the price of coffee decreases? Answer: Again, the answer depends on whether the consumer was already a cigarettes or coffee addict. Take the first case: if she is already a cigarette addict, then as the price of coffee falls,initially she will not switch out to coffee. Eventually however (even addicts respond to prices!) the addict responds to the low coffee prices . Thus, the cross demand curve for cigarettes with respect to coffee prices is: Figure 6 For the case where the consumer is already a coffee addict, the cross demand curve for cigarettes is simply nil and is depicted in Figure 7: ECO 204, 2008‐2009. Ajaz Hussain. Department of Economics, University of Toronto 6 Figure 7 (d) In part (a), what happens to coffee and cigarettes consumption as income increases? Answer: It again depends on whether the consumer was already a cigarettes or coffee addict. In Figure8‐‐ for the case when the consumer is already a cigarettes addict‐‐ more income results in more addictive smoking. In Figure 9‐‐ for the case when the consumer is already a coffee addict‐‐ more income results in more caffeine intake. ECO 204, 2008‐2009. Ajaz Hussain. Department of Economics, University of Toronto 7 Figure 8 Figure 9 (e) Will consumers engage in addictive behavior if coffee prices decrease with volume? Answer: As discussed in Lecture 2, it is possible to break addictive behavior so long as coffee prices increase (not decrease) with volume. For then, with one price “break” point, we’d have an opportunity to break the consumer’s vile addiction to coffee and cigarettes: ECO 204, 2008‐2009. Ajaz Hussain. Department of Economics, University of Toronto 8 Figure 10 To understand this budget line, note that cigarette prices are uniform (and therefore constant) while coffee prices are increasing with volume. For the first few units of coffee, the price of coffee is low; the price then increases over some units of coffee. Thus, the budget line slope (‐P1/P2 = ‐Pcoffee /Pcigarettes ) is initially flat and then steep. Question 2 (Based on Summer 2008 Final Exam Question) If Ajax if doesn’t have at least 5 pounds of food a day, he will die. In fact, with less than 5 pounds of food a day, he doesn’t care about anything else. Suppose that once he has the threshold level of food: (a) He prefers food and everything else as perfect complements. Characterize Ajax’s optimal choice‐‐ in particular, is it an interior or corner solution? What happens to his consumption of food and everything else as the price of food decreases? Answer: The indifference curves were done in HW 1. From these, we can examine the effect of lower food prices on quantities of food and everything else: ECO 204, 2008‐2009. Ajaz Hussain. Department of Economics, University of Toronto 9 Figure 11 Observe how below 5 lbs of food, the optimal choice is a corner solution after which it is an interior solution. From these optimal choices, the demand curve for food and cross‐ demand for everything else are: Figure 12 ECO 204, 2008‐2009. Ajaz Hussain. Department of Economics, University of Toronto 10 (b) He prefers food and everything else as imperfect substitutes with decreasing MRS. Characterize Ajax’s optimal choice‐‐ in particular, is it an interior or corner solution? What happens to his consumption of food and everything else as the price of food decreases? Answer: The indifference curves were done in HW 1‐‐ in Figure 13, I have drawn a specific case of imperfect substitute curves‐‐ you will get different results for other depictions of imperfect substitute preferences: Figure 13 From these, we can examine the effect of lower food prices on quantities of food and everything else, as shown in Figure 14. There, note, how as the price of food decreases, consumption of everything else is initially nil, but once Ajax has enough food to sustain himself, consumption of everything else increases, but there comes a point where it decreases: you should convince yourself of this through Figure 13. ECO 204, 2008‐2009. Ajaz Hussain. Department of Economics, University of Toronto 11 Figure 14 (c) He prefers food and everything else as perfect substitutes with MRS of ‐1. Characterize Ajax’s optimal choice‐‐ in particular, is it an interior or corner solution? What happens to his consumption of food and everything else as the price of food decreases? Answer: The indifference curves were done in HW 1‐‐ Figure 15 shows the effect of lower food prices. Beginning with high food prices, the optimal choices are initially corner solutions, followed by one particular price at which the budget line is tangent to the indifference curve (so that there will be an infinity of solutions), followed once again by corner solutions): ECO 204, 2008‐2009. Ajaz Hussain. Department of Economics, University of Toronto 12 Figure 15 Figure 16 (d) He prefers food and everything else as perfect substitutes with MRS of ‐1/2. Characterize Ajax’s optimal choice‐‐ in particular, is it an interior or corner solution? What happens to his consumption of food and everything else as the price of food ECO 204, 2008‐2009. Ajaz Hussain. Department of Economics, University of Toronto 13 decreases? Answer: Qualitatively, the solution looks the same as part (c). (e) He only cares about everything else. Characterize Ajax’s optimal choice‐‐ in particular, is it an interior or corner solution? What happens to his consumption of food and everything else as the price of food decreases? Answer: The indifference curves were done in HW 1 and are depicted in Figure 17 below: Figure 17 Observe how the solutions are corner solutions. Beginning from high food prices, as the price of food decreases, Ajax first only consumes food and once he reaches the threshold level of food, consumes only everything else. Thus, the demand and cross demand curves are: ECO 204, 2008‐2009. Ajaz Hussain. Department of Economics, University of Toronto 14 Figure 18 (f) He reaches a “bliss point” at 10 lbs of food a day and 5 units of everything else. Characterize Ajax’s optimal choice‐‐ in particular, is it an interior or corner solution? What happens to his consumption of food and everything else as the price of food decreases? Answer: I am going to assume that once Ajax has 5 lbs of food a day, his preferences are “circular” (see HW 1); with an alternative model of “bliss” preferences, you’ll get different results: ECO 204, 2008‐2009. Ajaz Hussain. Department of Economics, University of Toronto 15 Figure 19 Figure 20 ECO 204, 2008‐2009. Ajaz Hussain. Department of Economics, University of Toronto 16 Question 3 (Summer 2008 Final Exam Question) Meredith has preferences over wine and cheese represented by concentric circles centered around 10 units of cheese and wine. (a) Suppose her felicity is greatest at the center. What happens to Meredith’sconsumption of cheese as the price of cheese decreases? Answer: Here are Meredith’s preferences: Figure 21 From this, we have the demand curve for cheese: ECO 204, 2008‐2009. Ajaz Hussain. Department of Economics, University of Toronto 17 Figure 22 (b) Suppose her felicity is lowest at the center. What happens to Meredith’s consumption of cheese as the price of cheese decreases? Answer: Meredith’s preferences are depicted in Figure 23. Figure 23 ECO 204, 2008‐2009. Ajaz Hussain. Department of Economics, University of Toronto 18 From this, we have the demand curve for cheese: Figure 24 ECO 204, 2008‐2009. Ajaz Hussain. Department of Economics, University of Toronto ...
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This note was uploaded on 05/02/2011 for the course ECO 204 taught by Professor Hussein during the Fall '08 term at University of Toronto- Toronto.

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