A consumer is choosing between magazines and curves and budget constraint are shown on the graph to the right. 50- The utility-maximizing point is Point-B 45- 40- Suppose that the price of books falls. 35- 1.) Use the line drawing tool to draw a new budget constraint (still tangent to one of the indifference curves). Label this line 'L2 30- 2.) Use the point drawing tool to locate the new utility-maximizing point. Label this point 'T 25- 20- Carefully follow the instructions above, and only draw the required objects. 15- 10- 5- 22.5 0- 10 15 20 25 30 35 40 45 50 Books Magazines
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- 1. Mary has $100 to spend on goods X and Y. The price of Y is pY = $2.50. Mary has wellbehaved preferences and two of her indifference curves are shown on the above graph along with sometangent points. **This is a graphical problem. You may visually estimate (eyeball) any quantities you need.You may need to locate additional tangencies. a) Suppose the price of X is $1.25. On the graph above, label Mary’s budget line as (BLA) and label Mary’soptimal consumption bundle as bundle A. b) Now suppose the price of X rises to $5. On the graph above, label Mary’s budget line as (BLB) and labelMary’s optimal consumption bundle as bundle B. c) Next find the Hicks Compensated Bundle. To do this, put your ruler on budget line BLB and move yourruler in a parallel fashion until it just touches the indifference curve through bundle A. Label this tangencyas bundle C and draw the line tangent line, along with appropriate || parallel marks, and label this line asthe compensated budget line BLC. Please…John’s preferences for Orange (O) and lemons (L) are represented by the funtion U(O, L)= O+2L. The oranges cost £2 and the lemons £1. Given that John’s monthly income is £30 answer the following questions: What type of goods are oranges and lemons for John? What is the proportion to which John is willing to exchange Oranges for Lemons? Illustrate and solve graphically John’s utility maximization problem. If his income increases every month by £10, how will John’s consumption choice be affected? Illustrate graphically the income expansion path and the Engel curve for each good. How will an increase in the price of Lemons to £6 affect John’s optimal consumption choice? (John’s income is £30) Graph John’s demand curve for each good. Assume that John wins a voucher of £20, redeemable only in Oranges. How would this affect John’s utility? (Assume that prices and income are as described initially) Assume that John is presented with two options: an Orange voucher of £20 or just £6 to spend…ASAP 1. Consider a consumer with utility u(x1,x2) = .5lnx1 + .5lnx2 (b) Now, consider an equivalent representation of the above utility functionx51 x52 Does this utility function have the "increasing difference property"? Howabout the "strict increasing difference" property?
- a. Suppose Fiona’s income is $100 per week, which she allocates between chocolates and books. Chocolates cost $2 each. Books cost $10 each if she purchases between 1 and 5 books. If she purchases more than 5 books in a week, the price falls to $5 for the 6th book and all subsequent books. Draw the budget constraint. Is it possible that Fiona might have more than one utility-maximizing solution? b. Confirm that if a consumer’s utility function is described by U = 2X + Y, and prices are px = 2 and py = 1, there is no unique utility maximizing solution regardless of income level. What does this tell you about X and Y as commodities? (Hint: draw a graph showing a budget constraint and indifference curve using the information provided.)a. A consumer is willing to trade 3 units of x for 1 unitof y when she has 6 units of x and 5 units of y. She isalso willing to trade in 6 units of x for 2 units of y whenshe has 12 units of x and 3 units of y. She is indifferentbetween bundle (6, 5) and bundle (12, 3). What is theutility function for goods x and y? Hint: What is theshape of the indifference curve?b. A consumer is willing to trade 4 units of x for 1 unitof y when she is consuming bundle (8, 1). She is alsowilling to trade in 1 unit of x for 2 units of y when sheis consuming bundle (4, 4). She is indifferent betweenthese two bundles. Assuming that the utility function isCobb–Douglas of the form U (x, y) = xα y β, where α andβ are positive constants, what is the utility function forthis consumer?c. Was there a redundancy of information in part (b)? Ifyes, how much is the minimum amount of informationrequired in that question to derive the utility function?Assume Pat spends all of her allowance to purchase 4 apples and 4 candy bars. Pat's marginal utility of the fourth apple is 20 utils, and her marginal utility of the fourth candy bar is 40 utils. If an apple costs $1.00 and a candy bar $0.50, to maximize utility Pat should(A) purchase more apples and more candy bars(B) maintain the current purchase of 4 apples and 4 candy bars(C) purchase more apples and fewer candy bars(D) purchase fewer apples and more candy bars(E) purchase fewer apples and fewer candy bars
- Suppose a consumer has utility function U(X, Y) = X2/3Y1/3. Suppose the consumer has M =$90 to spend and the prices of goods X and Y are PX = $15 and PY = $6 . a. Carefully express the consumer’s choice problem, using the given information (this is whereyou write out the max operator, the choice variables, the objective function, and the budget constraint). b. Compute the absolute value of the consumer’s marginal rate of substitution, and inspect it todetermine the shape of the consumer’s indifference curves: C-shaped, linear, )-shaped, or some other shape.To show your work, neatly use the arrow argument, increasing X (↑) and decreasing Y (↓) to see whether|MRS(X, Y)| is diminishing along an indifference curve. c. If the indifference curves are C-shaped write out the budget line and the equal slopes conditionthat characterize an interior solution to the consumer’s choice problem. Use the particulars for the givenconsumer. Solve these conditions to find the interior solution. On the…The price of DVDs (D) is $20.00 and the price of CDs (C) is $20.00. Katrina has a budget of $100.00 to spend on the two goods. Suppose that she has already bought 1 DVD and 1 CD. In addition, there are 3 more DVDs and 3 more CDs that she would really like to buy. 1.) Using the line drawing tool, given the above prices and income, draw her budget line in the figure. Label this line 'L'. 2.) Using the point drawing tool, and considering what Katrina has already purchased and what she still wants to purchase, identify the three different bundles of CDs and DVDs that she could choose. Label these points 'bundle 1', 'bundle 2', and 'bundle 3'. (Assume that she cannot purchase fractional units)C) Draw the indifference curve associated with a utility level of 36 and the indifference curve associated with a utility level of 72. Are the indifference curves bowed in toward the origin? The utility that Ann receives by consuming food F and clothing C is given by ?(?, ?) = √?? 4 + ?. Food costs N$5.00 a unit, and clothing costs N$15.00 a unit. Ann’s income is N$1850.00
- 4 Assume that a person's utility over two goods is given by U(g1; g2) = g1 + ln g2. The price of good g1 is equal to p1 and the price of good g2 is p2. The total income of the individual is given by I. The marginal rate of substitution between g1 and g2 is given by 1/(1/g2). Then, the expressions for this person's (1) budget constraint, (2) budget line's slope (assume that, graphically, g1 is on the horizontal axis and g2 on the vertical axis), and (3) the person's demand function for g2 (that is, g2 as a function of price ratio) are respectively:22. Peanut butter (PB) sells for 10 dollars per pound and Oysters (O) sell for 50 dollars perpound. Suppose Pat buys 5 pounds of peanut butter and one pound of oysters each month.With this consumption bundle, his MRSP B,O = 3. Which of the following is true (assumingPat’s preferences satisfy all the basic assumptions of consumer theory)?(a) Pat could increase his utility by buying more oysters and less peanut butter.(b) Pat could increase his utility by buying more peanut butter and less oysters.(c) Pat could increase his utility by buying more peanut butter and more oysters.(d) Pat could increase his utility by buying less peanut butter and less oysters.7. A consumer has preferences for coffee and pancakes that are complete, continuous, transitive, monotonic, and convex. At her current consumption bundle on the budget line, you could take away a maximum of 2 cups of coffee if you give her 5 extra pancakes without changing her utility. The price of a cup of coffee is $4, and the price of a pancake is $1. Assume you graph pancakes on the X-axis and coffee on the Y-axis. At the current consumption bundle, the bang per buck is higher for pancakes than coffee, and the consumer’s indifference curve is flatter than her budget line. a. True b. False Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.