A consumer has an income of $400 and is deciding between two products: X and Y.Assume that the X product is the horizontal axis product. The price of X is $10 andthe price of Y is $2. Assume the consumer currently wants to consume 50 units ofproduct Y to maximize his utility.a) Write out the equation to this consumers budget line. What is the slope to thisbudget constraint?b) How much of X and Y will the consumer consume to maximize his utility subjectto his budget constraint.C) Now assume the price of X changes to $5 and price of Y and Income stays thesame. At the new price, the consumer wants to buy 60 units of product X tomaximize her utility given her budget How much X and Y will the consumerconsume to maximize utility. Sthe before and after the change of the budget constraint and indifference gra onthe same graph space. Show all necessary points. Label clearly.s. Drawd) Write out the expression of the utiity maximizing ruie here.?

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ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Consider a consumer with the utility function u(x1,x2) = x11/3 x22/3. a. Find the Marginal Utility for each good. b. Find the slope of one of this consumer's indifference curves c. Write down the consumer's budget constraint. d. What is the slope of this consumer's budget constraint? Show how you derived your answer
What is a budget constraint? A consumer has an income of $3000. Soda costs $3 per liter and cheese costs $6 per pound. Draw the consumer's budget constriaint with soda on the vertical axis. What is the slope of the budget constraint?
sketch a person’s indifference map and budget line for two goods, X on the horizontal axis and Y on the vertical axis. Mark the optimum consumption point. Now illustrate the following (you might need to draw a separate diagram for each): (a) A rise in the price of good X (a normal good), but no change in the price of good Y. (b) A shift in the person’s tastes from good Y to good X. (c) A fall in the person’s income and a fall in the price of good Y, with the result that the consumption of Y remains constant (but that of X falls).
Consider the single-good utility function u(x) = 3x². du(x) a) Find the marginal utility of x, MUx = dx b) Plot the utility function and marginal utility function on two separate graphs. c) Does this utility function satisfy the law of diminishing marginal utility? Explain.
A consumer has an income of $400 and is deciding between two products: X and Y. Assume that the X product is the horizontal axis product. The price of X is $10 and the price of Y is $2. Assume the consumer currently wants to consume 50 units of product Y to maximize his utility. a) Write out the equation to this consumers budget line. What is the slope to this budget constraint? b) How much of X and Y will the consumer consume to maximize his utility subject to his budget constraint. C) Now assume the price of X changes to $5 and price of Y and Income stays the same. At the new price, the consumer wants to buy 60 units of product X to maximize her utility given her budget. How much X and Y will the consumer consume to maximize utility. g in the before and after the change of the budget constraint and indifference graph on the same graph space. Show all necessary points. Label clearly. ead oubstitutiofs. Draw d) Write out the expression of the utiiity maximizing ruie here.?
What happens to the original budget line if the price of good ? falls to 4$? (i.e., Will there be a change in the slope and/or intercepts of the original budget line? If yes, what are those changes?). Interpret economically how the change in the price of good ? affects the consumption decision of the consumer.
A consumer has a budget of £12 to split between two goods: good 1 has a price of 2, good 2 has a price of 3. Write the consumer’s budget constraint algebraically. Convert this budget constraint into the formula for the budget line. Show this line on a suitably labelled graph. The consumer’s budget increases to £24. Show the effect of this change graphically. A consumer dislikes good 1, and dislikes good 2. Show these preferences on a suitably labelled graph with an indifference curve. Label the graph: which areas would be preferred to those on the line?
Question 3: Samantha has $3,000 to spend on two goods: sandwiches and beer. The price of a sandwich is $6 and price of a beer is $5. a) Draw Samantha's budget line. Put beer on the horizontal axis. b) If Samantha's optimal consumption bundle contains 400 sandwiches, how many beer does her optimal consumption bundle contain? Show her optimal consumption in the graph above. c) Draw Samantha's indifference curve crossing her optimal consumption bundle.
Consider Gary's utility function: U(X,Y) = 5 XY, where X and Y are two goods. If the individual consumed 10 units of X and received 250 units of utility, how many units of Y must the individual consume? 5 25 0 10
A consumer currently spends a given budget on two goods, X and Y, in such quantities that the marginal utility of X is 15 and the marginal utility of Y is 8. The unit price of X is $3 and the unit price of Y is $2. The utility-maximizing rule suggests that this consumer should Multiple Choice a. decrease consumption of product X and increase consumption of product Y. b. increase consumption of product X and increase consumption of product Y. c. decrease consumption of product Y and increase consumption of product X. d. stick with the current consumption mix because it yields maximum utility.
1) The equation that economists use to measure the utility from a bundle of goods is called the budget constraint a) true b) false

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