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ECO 303 1 of 3 Stony Brook University Fall 2016 Alejandro Melo Ponce ASSIGNMENT: MIDTERM I PREPARATION Due: Optional, but you should use it to prepare for the midterm. Instructions: This is an optional assignment whose purpose is to prepare you for the midterm. It consists of six problems. I strongly recommend that you attempt to prepare all questions. On Tuesday’s Midterm I will pick four questions at random from this assignment which you will need to answer. 1. Michele, who has a relatively high income I , has altruistic feelings toward Sofia, who lives in such poverty that she essentially has no income. Suppose Michele’s preferences are represented by the utility function UM .cM ; cS / D c 1�˛ M c ˛ S ; where cM and cS are Michele and Sofia’s consumption levels, appearing as goods in a standard Cobb-Douglas utility function. Assume that Michele can spend her income either on her own or Sofia’s consumption (though charitable donations) and that $1 buys a unit of consumption for either (thus, the “prices” of consumption are pM D pS D 1). (a) Argue that the exponent ˛ can be taken as a measure of the degree of Michele’s altruism by providing an interpretation of extreme values of ˛ D 0 and ˛ D 1. What value would make her a perfect altruist (regarding others the same as oneself)? (b) Solve for Michele’s optimal choices and demonstrate how they change with ˛. (c) Suppose that there is an income tax at rate �, i.e. net income now is just .1 � � /I: Solve for Michele’s optimal choices under the income tax rate. (d) Now suppose that besides the income tax rate �, there are charitable deductions, so that income spent on charitable deductions is not taxed. Argue that this amounts to changing the price pS from $1 to $.1 � � /. Solve for the optimal choices under both the income tax rate and charitable deductions. Does the charitable deduction have a bigger incentive effect on more or less altruistic people? 2. Suppose that a fast-food junkie derives utility from three goods—soft drinks .x/, hamburgers .y/, and ice cream sundaes .z/—according to the utility function U.x; y; z/ D x0:5y0:5.1 C z/0:5: Suppose also that the prices for these goods are given by px D 1; py D 4; and pz D 8 and that this consumer’s income is given by I D 8: (a) Show that, for z D 0, maximization of utility results in the same optimal choices as in the case of a Cobb-Douglas utility function U.x; y/ D x0:5y0:5. Show also th at any choice that results in z > 0 (even for a fractional z) reduces utility from this optimum. (b) How do you explain the fact that z D 0 is optimal here? (c) How high would this individual’s income have to be for any z to be purchased? 1 ECO 303 2 of 3 3. Consider the utility function u.x; y/ D .x C 2/.y C 3/; x � 0; y � 0 with the accompanying budget constraint: px x C py y � I; px ; py ; I > 0: (a) Fix a given utility level U > 0 and find an explicit expression for the indifference curve defined by the utility level U > 0. The ...

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ECO 303 1 of 3 Stony Brook University Fall 2016 Alejandro Melo Ponce ASSIGNMENT: MIDTERM I PREPARATION Due: Optional, but you should use it to prepare for the midterm. Instructions: This is an optional assignment whose purpose is to prepare you for the midterm. It consists of six problems. I strongly recommend that you attempt to prepare all questions. On Tuesday’s Midterm I will pick four questions at random from this assignment which you will need to answer. 1. Michele, who has a relatively high income I , has altruistic feelings toward Sofia, who lives in such poverty that she essentially has no income. Suppose Michele’s preferences are represented by the utility function UM .cM ; cS / D c 1�˛ M c ˛ S ; where cM and cS are Michele and Sofia’s consumption levels, appearing as goods in a standard Cobb-Douglas utility function. Assume that Michele can spend her income either on her own or Sofia’s consumption (though charitable donations) and that $1 buys a unit of consumption for either (thus, the “prices” of consumption are pM D pS D 1). (a) Argue that the exponent ˛ can be taken as a measure of the degree of Michele’s altruism by providing an interpretation of extreme values of ˛ D 0 and ˛ D 1. What value would make her a perfect altruist (regarding others the same as oneself)? (b) Solve for Michele’s optimal choices and demonstrate how they change with ˛. (c) Suppose that there is an income tax at rate �, i.e. net income now is just .1 � � /I: Solve for Michele’s optimal choices under the income tax rate. (d) Now suppose that besides the income tax rate �, there are charitable deductions, so that income spent on charitable deductions is not taxed. Argue that this amounts to changing the price pS from $1 to $.1 � � /. Solve for the optimal choices under both the income tax rate and charitable deductions. Does the charitable deduction have a bigger incentive effect on more or less altruistic people? 2. Suppose that a fast-food junkie derives utility from three goods—soft drinks .x/, hamburgers .y/, and ice cream sundaes .z/—according to the utility function U.x; y; z/ D x0:5y0:5.1 C z/0:5: Suppose also that the prices for these goods are given by px D 1; py D 4; and pz D 8 and that this consumer’s income is given by I D 8: (a) Show that, for z D 0, maximization of utility results in the same optimal choices as in the case of a Cobb-Douglas utility function U.x; y/ D x0:5y0:5. Show also th at any choice that results in z > 0 (even for a fractional z) reduces utility from this optimum. (b) How do you explain the fact that z D 0 is optimal here? (c) How high would this individual’s income have to be for any z to be purchased? 1 ECO 303 2 of 3 3. Consider the utility function u.x; y/ D .x C 2/.y C 3/; x � 0; y � 0 with the accompanying budget constraint: px x C py y � I; px ; py ; I > 0: (a) Fix a given utility level U > 0 and find an explicit expression for the indifference curve defined by the utility level U > 0. The ...

- 1. ECO 303 1 of 3 Stony Brook University Fall 2016 Alejandro Melo Ponce ASSIGNMENT: MIDTERM I PREPARATION Due: Optional, but you should use it to prepare for the midterm. Instructions: This is an optional assignment whose purpose is to prepare you for the midterm. It consists of six problems. I strongly recommend that you attempt to prepare all questions. On Tuesday’s Midterm I will pick four questions at random from this assignment which you will need to answer. 1. Michele, who has a relatively high income I , has altruistic feelings toward Sofia, who lives in such poverty that she essentially has no income. Suppose Michele’s preferences are represented by the utility function UM .cM ; cS / D c 1�˛ M c ˛ S ; where cM and cS are Michele and Sofia’s consumption levels, appearing as goods in a standard
- 2. Cobb-Douglas utility function. Assume that Michele can spend her income either on her own or Sofia’s consumption (though charitable donations) and that $1 buys a unit of consumption for either (thus, the “prices” of consumption are pM D pS D 1). (a) Argue that the exponent ˛ can be taken as a measure of the degree of Michele’s altruism by providing an interpretation of extreme values of ˛ D 0 and ˛ D 1. What value would make her a perfect altruist (regarding others the same as oneself)? (b) Solve for Michele’s optimal choices and demonstrate how they change with ˛. (c) Suppose that there is an income tax at rate �, i.e. net income now is just .1 � � /I: Solve for Michele’s optimal choices under the income tax rate. (d) Now suppose that besides the income tax rate �, there are charitable deductions, so that income spent on charitable deductions is not taxed. Argue that this amounts to changing the price pS from $1 to $.1 � � /. Solve for the optimal choices under both the income tax rate and charitable deductions. Does the charitable deduction have a bigger incentive effect on more or less altruistic people? 2. Suppose that a fast-food junkie derives utility from three goods—soft drinks .x/, hamburgers .y/, and ice cream sundaes .z/—according to the utility function U.x; y; z/ D x0:5y0:5.1 C z/0:5: Suppose also that the prices for these goods are given by px D
- 3. 1; py D 4; and pz D 8 and that this consumer’s income is given by I D 8: (a) Show that, for z D 0, maximization of utility results in the same optimal choices as in the case of a Cobb-Douglas utility function U.x; y/ D x0:5y0:5. Show also th at any choice that results in z > 0 (even for a fractional z) reduces utility from this optimum. (b) How do you explain the fact that z D 0 is optimal here? (c) How high would this individual’s income have to be for any z to be purchased? 1 ECO 303 2 of 3 3. Consider the utility function u.x; y/ D .x C 2/.y C 3/; x � 0; y � 0 with the accompanying budget constraint: px x C py y � I; px ; py ; I > 0: (a) Fix a given utility level U > 0 and find an explicit expression for the indifference curve defined by the utility level U > 0. Then, derive an explicit expression for the marginal rate of substitution between good x and good y. (b) Draw the indifference curve (for this associated level of utility U ) and carefully label the graph
- 4. and its elements. (c) Show that the utility function is strictly increasing (and hence monotone) in x and y. (d) Now formally state the utility maximization problem and briefly describe its content, in par- ticular what constitutes the choice variables, and what constitutes parameters. (e) Provide an argument why in the present utility maximization problem, we can restrict atten- tion to the case where the budget constraint holds as an equality. (The argument should not involve the explicit computation of the optimal choices.) 4. Consider the utility function U.x; y/ D min.2x C y; x C 2y/ (a) Draw the indifference curve for U.x; y/ D 20. Shade the area where U.x; y/ � 20. (b) For what values of px py will the unique optimum be x D 0? (c) For what values of px py will the unique optimum be y D 0? (d) If neither x and y is equal to zero, and the optimum is unique, what must be the value of x y ?
- 5. 5. Consider a consumer with a utility function U.x; y/ D e.ln.x/Cy/1=3. (a) What properties about utility functions will make th is problem easier to solve? (b) Which of the non-negativity input demand constraints will bind for small I ? (c) Derive the Marshallian demand functions and the indirect utility function (using the original utility function). (d) Derive the expenditure function in terms of the original utils u. 6. There are two goods, food and clothing, whose quantities are denoted by x and y and prices px and py respectively. There is a consumer whose income is denoted by I and utility by U: His utility function is U.x; y/ D p xy: (a) Find this consumer Marshallian demand functions. Find the indirect utility function and the expenditure function. (b) Initially I D 100; px D 1 and py D 1. What quantities does the consumer buy, and what is his resulting utility? (c) Now the price of food rises to px D 1:21, while income and the price of clothing are as before.
- 6. What quantities does the consumer buy and what is his resulting utility? 2 ECO 303 3 of 3 (d) Suppose the increase in the price of food was caused by the government levying a tax of 21% on food. What is the government revenue from this tax? Hint: At the new prices, calculate the optimal consumption bundles .x�; y�/. Then calculate .1:21 � 1/x�. (e) If the government wants to compensate the consumer by giving him some extra income, how much extra income would be needed to restore him to the old utility level. (Hint: Use the expenditure function.) Is the government’s revenue from the tax on good itself sufficient to provide this compensation? What is the economic intuition of your answer? (f) If the government tries to compensate the consumer by giving him enough extra income to enable him to purchase the same quantities as he did at the original income and prices of part (b), how much extra income would the government have to give him ? With this income and the new prices, what quantities will the consumer actually buy? What will be his resulting utility? 3
- 7. Unit 8 AB224 | Microeconomics Unit 8 Assignment: Break–even Price and Shut–down Price Name: Course Number and Section: AB224–0X Date: General Instructions for all Assignments 1. Unless specified differently by your course instructor, save this assignment template to your computer with the following file naming format: Course number_section number_Last_First_unit number 2. At the top of the template, insert the appropriate information: Your Name, Course Number and Section, and the Date 3. Insert your answers below, or in the appropriate space provided for in the question. Your answers should follow APA format with citations to your sources and, at the bottom of your last page, a list of references. Your answers should also be in Standard English with correct spelling, punctuation, grammar, and style (double spaced, in Times New Roman, 12–point, and black font). Respond to questions in a thorough manner, providing specific examples of concepts, topics, definitions, and other elements asked for in the questions. 4. Upload the completed Assignment to the appropriate Dropbox. 5. Any questions about the Assignment, or format questions, should be directed to your course instructor.
- 8. In this Assignment, you will be assessed on the following outcomes: AB224-3: Examine how changes in the cost of production affect pricing and production quantity decisions of a firm in a perfectly competitive market. GEL-8.5: Apply critical thinking to the field of study. Assignment In this Assignment, you will define and calculate the remaining six major cost elements of a business, when given the Total Costs and the Quantity Produced, as well as to use the computed costs to determine a minimum cost output level for that business. In addition, you will compute both the break-even price and the shut-down price for a hypothetical business in a perfectly competitive market, and determine if that business would incur an economic profit at various market prices, and should the firm continue to produce at each of those price levels. Questions Table 2.a. shows an LED light bulb manufacturer’s total cost of producing LED light bulbs. Table 2.a. Cases of LED light bulbs produced in an hour Total Cost 0 $4,500 10 $4,900 20 $5,100 30
- 9. $5,300 40 $5,400 50 $5,700 60 $6,700 70 $7,900 80 $9,700 90 $11,800 1. What is this manufacturer’s fixed cost? Explain why. 2. Assuming that you only know the Total Costs (TC) (as is shown in the Table 2.a. above) explain how you would calculate each of the following: a. Variable Cost (VC); b. Average Variable Cost (AVC); c. Average Total Cost (ATC);
- 10. d. Average Fixed Cost (AFC); and, e. Marginal Costs (of a single case). 3. In Table 3.a., for each level of output, insert into the table the values for: a. the Variable Cost (VC); b. the Average Variable Cost (AVC); c. the Average Total Cost (ATC); and, d. the Average Fixed Cost (AFC). Table 3.a. Cases of LED light bulbs produced in an hour Total Cost Variable Costs Average Variable Costs Average Total Costs Average Fixed Cost a. b. c. d. 0 $4,500 n/a n/a n/a 10 $4,900
- 12. 80 $9,700 90 $11,800 e. Given the information you computed in Table 3.a., what is the minimum cost output Level? Explain why. 4. Brenda Smith operates her own farm, raising chickens and producing eggs. She sells her eggs at the local farmers’ market, where there are several other egg producers’ also selling eggs by the dozen. (Brenda operates in a perfectly competitive market in which she is a “price taker.”) In order to make sure she does not lose money on selling eggs, she does an analysis of her costs for producing eggs as shown on Table 4.a. Table 4.a. Dozens of eggs Fixed Cost Total Cost Variable Costs Average Variable Costs per dozen Average Total Costs per dozen 0
- 14. $3.35 $48.00 $44.65 $0.74 $0.80 70 $3.35 $64.40 $61.05 $0.87 $0.92 80 $3.35 $80.00 $76.65 $0.96 $1.00 90 $3.35 $135.00 $131.65 $1.46 $1.50 a. What is Brenda’s break-even price for a dozen of eggs? Explain how you found that answer. b. What is Brenda’s shut-down price for a dozen of eggs? Explain how you found that answer. c. If the market price of a dozen eggs at the local farmers’ market is $1.45 per dozen, will Brenda make an economic profit? Explain how you determined your answer.
- 15. d. If the market price of a dozen eggs at the local farmers’ market is $1.45 per dozen, should Brenda continue producing eggs in the short run? Explain how you determined your answer. e. If the market price of a dozen eggs at the local farmers’ market is 72 cents per dozen, will Brenda make an economic profit? Explain how you determined your answer. f. If the market price of a dozen eggs at the local farmers’ market is 72 cents per dozen, should Brenda continue producing eggs in the short run? Explain how you determined your answer. g. If the market price of a dozen eggs at the local farmers’ market is 64 cents per dozen, will Brenda make an economic profit? Explain how you determined your answer. h. If the market price of a dozen eggs at the local farmers’ market is 64 cents per dozen, should Brenda continue producing eggs in the short run? Explain how you determined your answer. -------------------------------------------- References: Unit 8 Assignment: Break–even Price and Shut–down Price Grading Rubric: Content
- 16. Percent Possible Points Possible Full Assignment 100% 80 Overall Writing: 20% 16 Correct coversheet information at the top of 1st page 5% 4.00 APA format for answers 3% 2.40 Correct citations 3% 2.40 Standard English no errors 4% 3.20 At least one, or more, references 5% 4.00 Answers: provides complete information demonstrating analysis and critical thinking: 80% 64 Individual Questions:
- 17. 1. Calculate this manufacturer’s fixed cost 5% 4.00 2. a.–d. Define how this manufacturer’s variable cost, average variable cost, average total cost, average fixed cost, and marginal cost are calculated. 9% 7.20 3. a.–d. Compute this manufacturer's variable cost, average variable cost, average total cost, and average fixed cost 9% 7.20 3. e. Determine this manufacturer's minimum cost output level and explain. 6% 4.80 4. a. – Brenda's break-even price? 8% 6.40 4. b. – Brenda's shut-down price? 8% 6.40 4. c. – Any economic profit at $1.45 per dozen? 5% 4.00 4. d. – Continue producing at $1.45 per dozen? 6% 4.80 4. e. – Any economic profit at $0.72 per dozen? 6% 4.80 4. f. – Continue producing at $0.72 per dozen? 6% 4.80 4. g. – Any economic profit at $0.64 per dozen? 6%
- 18. 4.80 4. h. – Continue producing at $0.64 per dozen? 6% 4.80 Sub-total for Individual Questions: 80% 64 6 of 7