man2

Exercise #1. Annas preferences over consumption bundles (x1,x2) are summarized by the utility function U (x1,x2) = x1 (x2 + 1)2. (a) Derive an algebraic expression for the marginal utility MU1 (x1,x2) of good 1. (b) Derive an algebraic expression for the marginal utility MU2 (x1,x2) of good 2. (c) Use your answers from parts (a) and (b) to derive an algebraic expression for Annas marginal (e) Suppose now that Anna is currently consuming 27 units of good 1. How many units of good 2 must she consume in order to leave her just as well off as she was in part (c)? What is the value of Annas MRS at this consumption bundle? Compare your answer to the corresponding answer in part (c). Are your answers consistent with the convexity of Annas preferences? debt. Let xd denote how many millions of dollars are allocated to the payment of the national debt in 1999. The government can also contribute, to some extent, to its 1,000,000 citizens medical expenditures. The government has computed that during 1999 around 50% of its population will make an appointment (and only one) with a doctor. Each visit to a doctor costs B$100. The governments health plan will cover a certain fraction xh of the cost of a visit to a doctor. Notice that this variable is measured in percentage terms (e.g.: a value of 1 indicates 100% coverage). The constitution of Bahnanas grants the prime minister the authority of choosing xd and xh. His preferences over policy bundles (xd,xh) are represented by the Cobb-Douglas utility function: u (xd,xh) = 1000 x 1 2 d x 1 2h . (1) 1

Exercise #1. (a) For this question you could have proceeded in different ways: One way. Maximize a Cobb-Douglas utility function subject to the budget line: max xm,xc x0.1 m x0.9 c subject to 400 = xc + xm. First substitute the budget line in the utility function by replacing one of the variables, say xc, to get max xm h x0.1 m (400 xm)0.9 i . The rst-order condition for this maximization problem is 0.1x0.11 m (400 xm)0.9 0.9x0.1 m (400 xm)0.91 = 0. This can be simplied to yield: 0.1x1 m = 0.9 (400 xm)1 . Further simplication yields: 0.1 (400 xm) = 0.9xm xm = 40. Plugging this number in the equation for the budget line we get xc = 400 xm = 360. See Figure 1 for the graph. Another way. Another way to go is to recognize that Cobb-Douglas preferences satisfy all the assumptions we have mentioned in class (no boundary solutions, no kinks in indifference curves, convexity) that are necessary and sufficient for the optimal behavior of the consumer to be captured by the equality between the MRS and (minus) the price ratio MRS (xm,xc ) = pm pc . Notice that this condition is equivalent to the rst-order condition derived in the previous point. The marginal rate of substitution between xm and xc is just MRS (xm,xc) = 0.1 0.9 xc xm . 1 The ratio of the prices is just 1. Thus, at the optimal point: 0.1 0.9 xc xm = 1. Now you can replace the budget line into this expression to get rid of one of the variables. For example, by replacing xc we get 0.1 0.9 (400 xm) xm = 1. Rearranging: 0.1 (400 xm) = 0.9xm xm = 40. Plugging this number in the equation for the budget line we get xc = 400 xm = 360. See Figure 1 for the graph. (b) The equation for the budget line is 0.5xm + xc = 400if xm 50, xm + xc = 425if xm > 50. It is possible to nd this line by means of the following argument. If Anna does not buy any milk, then she can spend $400 on other things. The point (0,400) is therefore a point on the budget line. For each gallon of milk that Anna buys to a maximum of 50, she pays only 50 cents. If she consumes 50 gallons of milk, she pays $25 for them, and she is left with $375 to spend on the composite good. In other words, the point (50,375) is also a point on the budget line. In addition, all of the points on the line connecting (0,400) and (50,375) are on the budget line. The slope of this line segment is -1/2: for each extra gallon of milk, Anna has to reduce her expenditures on other things by 50 cents. Once Anna reaches the point (50,375), the slope of her budget line changes to -1 (i.e. the slope of the budget line in part (a)). This is because Anna does not receive discounts on gallons of milk beyond the 50-th. Finally, if Anna spends all her income on milk, she can buy 425 gallons of milk: in this case, Anna spends $25 for the rst 50 gallons, and the remaining $375 for the other 375 gallons (since the price is $1 after the 50-th gallon). All the points on the line connecting (50,375) and (425,0) are therefore on the budget line. The coordinates of the kink point are (50,375). See Figure 2 for the graph. (c) We need to show how to compute a compensating variation. The compensating variation is the amount of money - call it cv - that must be given to Anna after the price increase so that her utility is the same as before the price increase. When the milk price is $1 her utility is given by (see point a): u (40,360) = 400.13600.9. 2 To compute Annas utility when the milk price is $2 and she receives the transfer cv, we must nd how much milk and composite good she buys in those circumstances. In other words, we need to solve the optimization problem max xm,xc x0.1 m x0.9 c subject to 400 + cv = 2xm + xc. The optimal amounts xc (cv) and xm (cv) that Anna chooses of course depend on cv. Her utility will also depend on cv: u (xm (cv) ,xc (cv)) = (xm (cv))0.1 (xc (cv))0.9 . Now, to nd cv set u (40,360) = u (xm (cv) ,xc (cv)) . This is one equation in one unknown (cv), which can be solved for cv. Exercise #2. (a) Beer is an ordinary good because its demand increases when its price decreases. (b) Beer is a substitute for wine because as the price of wine goes up, demand for beer increases. (c) The relative price of a gallon of beer in terms of bottles of wine is pb pw = $15 $10 = 1.5. (d) The demand function for beer is: xb = 110 2pb. To plot the demand curve we need to compute the inverse demand function: pb = 55 1 2 xb. See Figure 2 for a plot of this function. The loss in consumers surplus is given by the sum of the shaded areas of the rectangle and the triangle in gure 2: the area of the rectangle is 70(5) = 350. The area of the triangle is given by (80 70)5/2 = 25. Summing up these two areas we get that the loss in consumers surplus is $375. (e) The rectangular subregion represents the loss of surplus on the gallons that John now buys at a higher price. The triangular subregion represents the loss in surplus due to the fact that John reduces his demand for beer after the price increase. Exercise #3. (a) TRUE. See Figure 3. In this gure, and in this discussion I am assuming that the tax revenues are kept the same across these two tax experiments [If tax revenues were not the same of course this statement could easily be proved false.] The intuition here is that, when preferences are of the perfect complement type, the indifference curves display a kink at the bundle where the consumer is making the optimal choice. Thus, there is no tangency between the 3 budget line and the marginal rate of substitution at the optimal point. This tangency condition was responsible for the loss in consumers utility in the example we saw in class where indifference curves were smooth. In that example, from the tangency condition MRS (x1,x2) = p1 + t p2 we could see that the presence of the tax gave incentives to the consumer to decrease his consumption of good 1 with respect to the situation where income was taxed. When income is taxed the optimality condition reads: MRS (x1,x2) = p1 p2 and the tax does not distort the consumers choice between the two goods. (b) FALSE. All our assumptions on preferences cannot rule out the existence of Giffen goods, i.e., goods whose demand increase as their price increases. (c) FALSE. The marginal rate of substitution measures the rate at which the consumer, and not the market, is willing to substitute one good for the other. (d) FALSE. An indifference curve represents the collection of all bundles among which the consumer is indifferent. (e) FALSE. A lump sum subsidy to a consumer does not affect the relative price of the goods the consumer is buying. Therefore it does not affect the optimality condition MRS = p1/p2. However, it does affect the consumers behavior because after the subsidy the consumer is going to buy more of at least one of the goods under consideration (because he has more money to spend, or some food coupons as in the Food Stamp program). 4

Read Case 5-1: Netflix on pages 181-182. Complete one of the following for your original post. Responses to peers can include additional examples from personal experience, additional support for choices, or questions about choices.

Answer at least one of the Case Questions. Include support, definitions, and specific examples from the case. (Check previous posts to avoid redundancy and ensure all questions are answered.) Conduct a SWOT analysis identifying at least 2 factors for each quadrant or create a BCG matrix identifying one item for at least three of the quadrants. Be sure to support your choices. Conduct online research and report back with the latest on Netflix. Topics can include current news related to future plans, new product offerings, new management, expansions, how COVID 19 has impacted them, etc. Be sure to site your source(s). Minimum,

oject 1

This project will enable you to demonstrate skill and underpinning knowledge, and produce end products suitable for use in the work place. (If you are not working you will need to discuss, with your assessor, how you can address this as a simulation or possibly how you can address it in terms of a company for which you have previously worked.)

You must develop a business plan.

The plan must be clearly articulated and formatted in such a way that makes it acceptable to the business organisation. It must contain all of the necessary elements and must be informed by accurate, current, relevant and useful data/ information. Graphs, charts, tables etc can be used and any information that is relevant but not necessarily required for inclusion in the plan can be included in an appendix.

The plan could apply to the business as a whole; specific aspects of the business, or to a proposed new venture.

Submit, to your assessor, the completed business plan, relevant risk and cost-benefit analyses and brief answers to the following questions:

What concepts and ideas were considered? How did you identify the resources that would be required to support plan? What personnel would be involved in the planning process? What data/ information did you use when formulating the plan? With whom did you consult and why did you consult with these people? From what sources did you gather data/ information? How did you verify the currency, reliability and usefulness of the data/ information you collected? How will the plan benefit the business? How will you communicate this plan to other personnel in the business and how will you ensure that they support the plan? Will the plan make any differences to the skills and competencies required by employees; and if it does, what action will you take? How will the plan contribute to continuous improvement? a business plan that you have written data you have collected and analysed for contribution to a business plan organisational performance reports that are mapped against planned business objectives the results of SWOT or other research and planning activities market research that you have undertaken a portfolio of evidence showing a range of business planning activities in which you were involved, and their outcomes third party workplace reports of on-the-job performanceto show that you are able to effectively develop and implement business plans

Exercise #1. Anna consumes two goods: milk (measured in gallons) and a composite good (measured in dollars). Let xm represent the gallons of milk that Anna consumes in a given month and let xc represent her expenditures on the composite good in a given month. Annas preferences over consumption bundles (xm,xc) are summarized by the utility function: u (xm,xc) = x0.1 m x0.9 c . Annas monthly income is $400. Let pm denote the dollar price of a gallon of milk. (a) [10 pts.] Suppose that pm = $1. What is Annas optimal consumption bundle? Show your work. Illustrate your answer with a neat and clear diagram showing Annas budget line and indifference curves. Label the points at which the budget line intersects the axes and identify the optimal bundle. (b) [10 pts.] Suppose now that the local grocery store where Anna regularly shops decides to introduce a discount on milk. Specically, for each gallon of milk that Anna buys, the grocery store reduces its price from $1 per gallon to $0.50 per gallon, up to a maximum number of 50 gallons of milk per month. If Anna buys more than 50 gallons she has to pay the regular price on every gallon beyond the 50-th. In a neat and clear diagram, graph Annas budget line. Label the points at which the budget line intersects the axes and determine the coordinates of the kink point. (c) [15 pts.] Suppose now that the price of milk is again pm = $1 (there are no discounts anymore). Due to a shortage of milk, the price of milk increases from $1 to $2. Describe how to compute the extra income that must be given to Anna in order to compensate her for this increase in the price of milk (i.e., the compensating variation) [Here you are not asked to compute this amount. Simply show which steps you would take to compute it.] Exercise #2. John has the following demand function for beer xb = m 2pb + pw where xb denotes the gallons of beer he demands per month, pb is the dollar price of a gallon of beer, pw is the dollar price of a bottle of wine, and m denotes Johns income. (a) [5 pts.] Is beer an ordinary good in this case? Motivate your answer. [Notice: no credit will be given to yes/no type of answers. In order to get credit you need to explain your answer.] 1 (b) [5 pts.] Is beer a substitute for wine in this case? Motivate your answer. [Notice: no credit will be given to yes/no type of answers. In order to get credit you need to explain your answer.] (c) [5 pts.] Suppose that the price of a bottle of wine is pw = $10, and the price of a gallon of beer is pb = $15. What is the relative price of a gallon of beer in terms of bottles of wine? (d) [10 pts.] Suppose that m = $100 and that pw = $10. Compute the loss in Johns consumer surplus that occurs when the price of a gallon of beer increases from $15 to $20. Support your analysis with a graph representing Johns demand curve and his loss in consumers surplus. [Remember that to draw a demand curve you need to place pb on the y-axis and xb on the x-axis.] (e) [10 pts.] From point (d) you can see that the loss in consumers surplus can be decom- posed into two subregions, whose shapes are respectively rectangular and triangular. How can you interpret each of these two subregions? Exercise #3. Consider the following statements and say whether they are true or false and why. To get credit you should provide a clear justication for your answers. (a) [10 pts.] If two goods are perfect complements the consumer will be just as well off facing a quantity tax as an income tax. (b) [5 pts.] If the price of one good increases the demand for that good always decreases. (c) [5 pts.] The marginal rate of substitution measures the rate at which the market is willing to substitute one good for the other. (e) [5 pts.] An indifference curve represents the collection of all bundles that a consumer can buy. (f) [5 pts.] Bydenition, a lump sum subsidy to a consumer does not affect his/her consumption behavior.

Exercise #1. (a) For this question you could have proceeded in different ways: One way. Maximize a Cobb-Douglas utility function subject to the budget line: max xm,xc x0.1 m x0.9 c subject to 400 = xc + xm. First substitute the budget line in the utility function by replacing one of the variables, say xc, to get max xm h x0.1 m (400 xm)0.9 i . The rst-order condition for this maximization problem is 0.1x0.11 m (400 xm)0.9 0.9x0.1 m (400 xm)0.91 = 0. This can be simplied to yield: 0.1x1 m = 0.9 (400 xm)1 . Further simplication yields: 0.1 (400 xm) = 0.9xm xm = 40. Plugging this number in the equation for the budget line we get xc = 400 xm = 360. See Figure 1 for the graph. Another way. Another way to go is to recognize that Cobb-Douglas preferences satisfy all the assumptions we have mentioned in class (no boundary solutions, no kinks in indifference curves, convexity) that are necessary and sufficient for the optimal behavior of the consumer to be captured by the equality between the MRS and (minus) the price ratio MRS (xm,xc ) = pm pc . Notice that this condition is equivalent to the rst-order condition derived in the previous point. The marginal rate of substitution between xm and xc is just MRS (xm,xc) = 0.1 0.9 xc xm . 1 The ratio of the prices is just 1. Thus, at the optimal point: 0.1 0.9 xc xm = 1. Now you can replace the budget line into this expression to get rid of one of the variables. For example, by replacing xc we get 0.1 0.9 (400 xm) xm = 1. Rearranging: 0.1 (400 xm) = 0.9xm xm = 40. Plugging this number in the equation for the budget line we get xc = 400 xm = 360. See Figure 1 for the graph. (b) The equation for the budget line is 0.5xm + xc = 400if xm 50, xm + xc = 425if xm > 50. It is possible to nd this line by means of the following argument. If Anna does not buy any milk, then she can spend $400 on other things. The point (0,400) is therefore a point on the budget line. For each gallon of milk that Anna buys to a maximum of 50, she pays only 50 cents. If she consumes 50 gallons of milk, she pays $25 for them, and she is left with $375 to spend on the composite good. In other words, the point (50,375) is also a point on the budget line. In addition, all of the points on the line connecting (0,400) and (50,375) are on the budget line. The slope of this line segment is -1/2: for each extra gallon of milk, Anna has to reduce her expenditures on other things by 50 cents. Once Anna reaches the point (50,375), the slope of her budget line changes to -1 (i.e. the slope of the budget line in part (a)). This is because Anna does not receive discounts on gallons of milk beyond the 50-th. Finally, if Anna spends all her income on milk, she can buy 425 gallons of milk: in this case, Anna spends $25 for the rst 50 gallons, and the remaining $375 for the other 375 gallons (since the price is $1 after the 50-th gallon). All the points on the line connecting (50,375) and (425,0) are therefore on the budget line. The coordinates of the kink point are (50,375). See Figure 2 for the graph. (c) We need to show how to compute a compensating variation. The compensating variation is the amount of money - call it cv - that must be given to Anna after the price increase so that her utility is the same as before the price increase. When the milk price is $1 her utility is given by (see point a): u (40,360) = 400.13600.9. 2 To compute Annas utility when the milk price is $2 and she receives the transfer cv, we must nd how much milk and composite good she buys in those circumstances. In other words, we need to solve the optimization problem max xm,xc x0.1 m x0.9 c subject to 400 + cv = 2xm + xc. The optimal amounts xc (cv) and xm (cv) that Anna chooses of course depend on cv. Her utility will also depend on cv: u (xm (cv) ,xc (cv)) = (xm (cv))0.1 (xc (cv))0.9 . Now, to nd cv set u (40,360) = u (xm (cv) ,xc (cv)) . This is one equation in one unknown (cv), which can be solved for cv. Exercise #2. (a) Beer is an ordinary good because its demand increases when its price decreases. (b) Beer is a substitute for wine because as the price of wine goes up, demand for beer increases. (c) The relative price of a gallon of beer in terms of bottles of wine is pb pw = $15 $10 = 1.5. (d) The demand function for beer is: xb = 110 2pb. To plot the demand curve we need to compute the inverse demand function: pb = 55 1 2 xb. See Figure 2 for a plot of this function. The loss in consumers surplus is given by the sum of the shaded areas of the rectangle and the triangle in gure 2: the area of the rectangle is 70(5) = 350. The area of the triangle is given by (80 70)5/2 = 25. Summing up these two areas we get that the loss in consumers surplus is $375. (e) The rectangular subregion represents the loss of surplus on the gallons that John now buys at a higher price. The triangular subregion represents the loss in surplus due to the fact that John reduces his demand for beer after the price increase. Exercise #3. (a) TRUE. See Figure 3. In this gure, and in this discussion I am assuming that the tax revenues are kept the same across these two tax experiments [If tax revenues were not the same of course this statement could easily be proved false.] The intuition here is that, when preferences are of the perfect complement type, the indifference curves display a kink at the bundle where the consumer is making the optimal choice. Thus, there is no tangency between the 3 budget line and the marginal rate of substitution at the optimal point. This tangency condition was responsible for the loss in consumers utility in the example we saw in class where indifference curves were smooth. In that example, from the tangency condition MRS (x1,x2) = p1 + t p2 we could see that the presence of the tax gave incentives to the consumer to decrease his consumption of good 1 with respect to the situation where income was taxed. When income is taxed the optimality condition reads: MRS (x1,x2) = p1 p2 and the tax does not distort the consumers choice between the two goods. (b) FALSE. All our assumptions on preferences cannot rule out the existence of Giffen goods, i.e., goods whose demand increase as their price increases. (c) FALSE. The marginal rate of substitution measures the rate at which the consumer, and not the market, is willing to substitute one good for the other. (d) FALSE. An indifference curve represents the collection of all bundles among which the consumer is indifferent. (e) FALSE. A lump sum subsidy to a consumer does not affect the relative price of the goods the consumer is buying. Therefore it does not affect the optimality condition MRS = p1/p2. However, it does affect the consumers behavior because after the subsidy the consumer is going to buy more of at least one of the goods under consideration (because he has more money to spend, or some food coupons as in the Food Stamp program). 4