3. Nathaniel must divide PHP 500 between the consumption of product X and product Y. The relevant market prices are Px=50 and P=20. a. Write the equation for the consumer's budget line. Interpret the equation. b. Illustrate the consumer's opportunity set in a carefully labeled diagram, where X lies on the x-axis while Y lies on the y-axis. Interpret the consumer's opportunity set. c. Given the following indifference curves, the budget and the prices of goods X and Y, at what point is the optimal choice? Explain your answer.

3. Nathaniel must divide PHP 500 between the consumption of product X and product Y. The relevant market prices are Px=50 and P=20. a. Write the equation for the consumer's budget line. Interpret the equation. b. Illustrate the consumer's opportunity set in a carefully labeled diagram, where X lies on the x-axis while Y lies on the y-axis. Interpret the consumer's opportunity set. c. Given the following indifference curves, the budget and the prices of goods X and Y, at what point is the optimal choice? Explain your answer.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter3: Preferences And Utility

Section: Chapter Questions

Problem 3.9P

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The graph of the budget line below has dollars on the vertical axis and food on the horizontal axis. Which statement is false? D 100 Food The vertical intercept represents all money available for purchasing. The distance OA shows the amount of money spent on OD amount of food. If the amount of money available is known in this graph, then the absolute and relative price of food is known also. The horizontal intercept represents all the food the consumer could purchase with the budget available.
Refer to the indifference curve/budget line diagram below in Figure 7. Given that a consumer initially faces budget line (BL1) and ICI, and thus, by choosing consumption point c, is able to achieve the optimal utility level. If the price of x (Px) decreases, then the substitution effect (SE) is the movement from _-. effect (IE) is the movement from and the income y a IC2 d IC: BLI Figure 7 O a. from b to a; and a to d. O b. from a to b; and b to c. O c. No correct answwers. O d. from c to d; and d to a.
A consumer is choosing between magazines and books. His indifference curves and budget constraint are shown on the graph to the right. 50- 45- The utility-maximizing point is Point-B 40 Suppose that the price of books falls. 35 .... 1.) Use the line drawing tool to draw a new budget constraint (still tangent to 30- one of the indifference curves). Label this line 'L2 25- 2.) Use the point drawing tool to locate the new utility-maximizing point. Label this point 'T 20- Carefully follow the instructions above, and only draw the required objects. 15- 10- 5- 22.5 0- 35 20 25 Books 15 40 45 50 étv 15 MacBook Air 80 DII esc F2 F3 F5 F6 F7 F8 F1 ! @ $ 1 4 6. 7 8 9 Q W E IT Y tab A F つ K caps lock Z C V shift fn control option command つ Magazines N リ
Question 7: For each of the following price-income scenarios, sketch the con- sumer's budget lines on one set of axes (i.e. put all three budget lines in one picture and label them 1, 2, and 3). Y is income, and pı and p2 are the prices of goods 1 and 2, respectively. (1) Y = 70, p1 = 5, p2 = 10 (2) Y = 70, p1 = 10, p2 = 10 (3) Y = 140, p1 = 10, p2 = 10 For the prices and income in part (1), solve for the optimal bundle for a con- sumer with each of the following utility functions: (i) U(q1, 42) = min{q1,5q2}; (ii) U (q1, 42) = 391 + 4q2; and (iii) U(41, 42) = q" 42 3/7 4/7 4 In each case, how would the optimal amounts of each good change if the prices and income were to change to those given in part (2)?
Mega Partner is selling two products Marker(m) and Eraser(e) and their budget is given with thefollowing equation: 15Qe+ 30Qm= 3000. Now answer the following questions. I. Draw the budget line for Mega PartnerII. What would be the highest amount spend on Marker with the existing budgetIII. If Total budget increases to 4500 what would be the new budget line (use diagram)IV. If Price of the Marker becomes 15, how this changes the existing budget line keeping allthe values remain same.
please only do: if you can teach explain each partc: what does it mean? can you show graphs: For these to be optimal choices with such preferences, the indifference curve through a must lie entirely on or above the budget line associated with (p, w), and simi- larly for r' for the budget line associated with (p', w'). how do you know this:Because each of these bundles lies below the other budget line, this implies that the indifference curves must cross, which is impossible. can you show graphs: note that (3,1) is a conver combination of x and x', so for conver preferences must be weakly preferred to x (the less preferred bundle between a and a'). But then the bundle (3,5/3) must be strictly preferred z, contradicting that is optimal given the initial budget set
1 . Assume the budget constraint and the indifference curves are both linear. Assume the consumer is willing to tradeoff 1 of good X for 1 of good Y. If the relative price of one additional good X is giving up 1/2 of good Y, then the optimal bundle of the two goods is? Assume the budget constraint and the indifference curves are both linear. Assume the consumer is willing to tradeoff 1 of good X for 1 of good Y. If the relative price of one additional good X is giving up 1/2 of good Y, then the optimal bundle of the two goods is? Assume the government imposes an effective minimum wage (i.e., one above the equilibrium wage rate that would otherwise prevail in that market). Our supply and demand analysis implies? If preferences for pizza increase and the price of labor to produce pizza decreases, the equilibrium quantity of pizza will ____ and the equilibrium price of pizza will _____ .? Assume an intertemporal budget constraint that shows how consumption can be traded off between…
A 2015 report by the music industry estimated the revenue lost to the industry every yearfrom illegal downloading. In this problem we will derive some of the estimates that may havegone into their calculation (approximately).First, start with the individual consumer’s problem. Suppose a typical consumer has a yearlyentertainment budget of I that they can allocate between music downloads (D) and otherforms of entertainment (E). Consumer preferences are characterized by a utility functionU(D, E). a.) Write an expression for the consumer’s budget constraint as a function of their entertainment budget and the prices of music downloads (Pd ) and other entertainment (Pe). (b) Write the consumer’s constrained optimization problem in Lagrangian form. (Note: Youdo not need to solve it or derive first order conditions.)
Assume, for simplicity, consumers in the United States only purchase food and all other goods with food plotted along the horizontal axis. During the COVID-19 stay-at-home mandate, Congress passed an economic stimulus package paying $1,200 to each person. How does this affect the budget line for each consumer? A. Makes the budget line steeper. B. Makes the budget line flatter. O C. Parallel outward (rightward) shift. D. Parallel inward (leftward) shift. E. None of the above.
2. Suppose a consumer has a fixed budget of $200, and she spends it all on two goods, x, and x2. The price of x, is $40 per unit and the price of x2 is $20 per unit; x1 and x2 are normal goods. (a) Draw and label the consumer's budget constraint, with x1 on the horizontal axis and x2 on the vertical axis. (b) What is the value of the consumer's marginal rate of substitution at her optimal con- sumption bundle? Explain what you your answer means. (e) Suppose the price of x, increases to $25 per unit. Graphically show the effect of this price change on the consumer's budget constraint.
4. Suppose a person has $8 to spend only on apples and bananas. Apples 1 cost $0:4 each, and bananas cost $0:1 each. Furthermore, his preferences for apples (A) and bananas (B) can be represented by U = pAB. a) If A = 5 and B = 80, what will utility be?b) If A = 10, what value of for B will provide the same utility in part a? c) If A = 20, what value of for B will provide the same utility in parts a and b?d) Graph the indi§erence curve implied by parts a through c.e) Give the budget constraint, which of the points identiÖed in parts a through c can be bought by this person?f) show through some examples that every other way of allocating income provides less utility than does the point identiÖed in part b. graph this utility maximizing situation.
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?