Fluent Essays

you have to be familiar with utility functions and graphing themplease look at the file carefully and answer all the questions ask me if there is any questions _w20_hw_1.docx Unformatted Attachment Preview 1. Warm up questions. a. Preference maps: i. Draw the usual preference map with three indifference curves for food and AOG with food on the horizontal axis. Add a budget constraint that allows you to maximize utility at the middle indifference curve. ii. Draw a preference map with three indifference curves of a good that you are indifferent to (neither like or dislike) on the horizontal axis and AOG. Add a budget constraint that allows you to maximize utility at the middle indifference curve. b. Budget constraint: Consider a person with $120 that buys AOG for $1 and drinks for $5. i. Graph the budget constraint and label the intercepts and slope on two different graphs. ii. Graph a new budget constraint on one of the axes from i if income changes to $150. iii. Graph a new budget constraint on the other axis if the price of drinks changes to $8 (income is still $120). c. Constrained optimization: Consider a utility function of U = D1/4AOG1/2, where D is drinks and AOG is all other goods. i. Find the demand functions for D and AOG as a formula using M = PDD + PAAOG. ii. Substitute in values M = $120, PD = $5, and PA = $1 to find the optimal bundle. iii. What would be the new quantity of D and AOG if M increased to $150? iv. What would be the new quantity of D and AOG if PD = $8 with M = $120? 2. Sketch indifference curves for each of the following consumers for a day’s worth of coffee and food, and describe why the indifference curves take the shape they do. Draw the indifference curves as how they would look if the drank a range of 0 to 4 cups. a. Ron treats coffee and food as ordinary goods, but is neutral to coffee beyond 3 cups. b. For Gareth, food is always an ordinary good where more is better; however, coffee is an ordinary good up to 2 cups but then becomes a bad after two cups. c. Julie only wants coffee and doesn’t care about food until she has had 2 cups of coffee, after that both goods become ordinary goods. 3. It is common for individuals and small businesses to join stores like Costco to get lower prices. Suppose a consumer joins Costco at a cost of $60 for an annual membership. Assume that $1,000 is their allotted budget for goods at Costco and/or at all other stores, but the stores offer the same goods. To simplify assume that you can purchase goods at Costco and all other stores in $1 increments. a. Graph the “budget constraint” for someone that does not join Costco on a graph with Costco and All other Stores. This is a little tricky, consider how many goods are bought from All other Stores and Costco if they do not join Costco and quantify the intercept. b. On the same graph, draw the budget constraint for someone that joins Costco assuming Costco prices are 20\% less expensive than all other stores. If they join they can purchase at Costco and All other Stores. Quantify the intercepts and slope of the new constraint. c. Not everyone is made better off by joining Costco. Draw an indifference curve for someone that would be indifferent to joining Costco. This is a bit tricky, remember part a. d. How much has to be spent at Costco to break-even for joining? 4. Evan has a choice of eating cookies or broccoli, but gives up play time to do so. (Treat playtime as money that can be interpreted as income or prices. When my son Evan was young he would run around rather than eat with us. We threatened to reduce his desert if he ran around during dinner. Of course this threat was not credible so it did not work.) a. Currently his marginal utility from broccoli is 15 and from cookies is 10. For each unit of broccoli or cookies he eats he gives up 5 units of play time. Should his consumption change? Explain using the last dollar rule (the text refers to this as the use the graphs method on page 35). Note, you do not have enough information to find an optimal bundle, you can only say if his bundle is optimal or not and how he should change consumption of each good if it is not optimal (not how much he should change it) b. Suppose he gets less play time (income) and eats the same amount of cookies, but less broccoli. Can you tell if cookies and broccoli are normal, inferior, or income neutral? c. Graph the change in part b. 5. Katie enjoys downloading music tracks and attending live music. She pays PD = $1 per downloaded song and PL = $10 per unit of live music (entrance fees to clubs). She has $90 per month to spend on music. Her utility function for music is U = D1/3L2/3, where D represents the quantity of downloaded songs and L is live shows. a. Use either the Last Dollar Rule (use-the-graphs pg 35) to find Katie’s optimal mix of music. b. What is Katie’s level of utility at the optimal mix? c. One of the weaknesses of using actual dollar values for prices and income is that you cannot find Engle and Demand functions. Go back to part a, but use the parameters M for income, PD for price of downloaded songs and PL for price of live music and solve for the demand of downloaded songs, QD = DD(PD, PL, M). d. Use the functions you found in part c to take derivatives to show mathematically if downloaded songs are: i. Normal or inferior? ii. Ordinary or Giffen goods? iii. Are downloaded songs and live shows substitutes, compliments or unrelated? Note, the derivative of DD(M, PD, PL) with respect to PD is tricky, so don’t worry if you have difficulty, give it your best try but don’t stress out. e. Graph the Engle curve and the Demand curve for Downloaded songs on separate axis using several prices and income levels. f. Find the income elasticity of demand using the Dd function you found in part c and a formula similar to the one two-thirds down on page 58 in the text. g. The hardest relationship/function to find in this problem is the utility function (income and prices are easily observable). How would you set up an experiment to gather data on someone’s utility function? ... Purchase answer to see full attachment