1. A consumer plans to spend a total of $300 (M) on goods X and Y. X costs $5 and Y costs $6. a) Draw the consumer’s budget constraint on a graph, labeling the intercepts. What is the name of the slope, the formula for the slope, and the number of this particular slope? b) The consumer has a utility function of U = 3X.4Y.6. (Note that these exponents are 0.4 and 0.6.) Find the point on the budget constraint that maximizes their utility. This will be the point where the slope of the indifference curve equals the slope of the budget constraint. You will need to use marginal utilities to find the optimizing ratio of one good to another, and then use the BC to find the actual numbers for each good. 2. a) Draw a budget constraint for a consumer who spends $200 on X and Y. Each good costs $4. b) Now assume that the consumer purchases 20 units of X; how many units of Y will they purchase? Draw a typical (convex) indifference curve that is consistent with these preferences. c) Suppose the price of X falls, so that it now costs $2. What is the new BC? d) Use your graph to clearly show the substitution effect. Once you have found that point, use your graph to show the income effect, with the range of possible utility-maximizing outcomes assuming each good is a normal good. Can we tell if the person will purchase more X? Can we tell if the person will buy more Y? 3. Do problem 2 over again, except that instead of the price of X falling to $2, the price of Y rises to $6. 4. a) For a demand curve Q(d) = 600 – 15*P, find the quantity demanded and total revenue paid for prices of $30, $25, $15, and $5. b) In each case, reduce the price by $0.50 and calculate the new amount of total revenue. Calculate how much the total revenue changed in each case if price falls by that amount. c) Calculate the elasticity of demand at each of the four original prices. Which price or prices should the firm NOT charge, and why?

Microeconomics A Contemporary Intro

10th Edition

ISBN:9781285635101

Author:MCEACHERN

Publisher:MCEACHERN

Chapter6: Consumer Choice And Demand

Section: Chapter Questions

Problem 2QFR

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Related questions

Question

1. A consumer plans to spend a total of $300 (M) on goods X and Y. X costs $5 and Y costs $6.

a) Draw the consumer’s budget constraint on a graph, labeling the intercepts. What is the name of the slope, the formula for the slope, and the number of this particular slope?

b) The consumer has a utility function of U = 3*X.4*Y.6. (Note that these exponents are 0.4 and 0.6.) Find the point on the budget constraint that maximizes their utility. This will be the point where the slope of the indifference curve equals the slope of the budget constraint. You will need to use marginal utilities to find the optimizing ratio of one good to another, and then use the BC to find the actual numbers for each good.

2. a) Draw a budget constraint for a consumer who spends $200 on X and Y. Each good costs $4.

b) Now assume that the consumer purchases 20 units of X; how many units of Y will they purchase? Draw a typical (convex) indifference curve that is consistent with these preferences.

c) Suppose the price of X falls, so that it now costs $2. What is the new BC?

d) Use your graph to clearly show the substitution effect. Once you have found that point, use your graph to show the income effect, with the range of possible utility-maximizing outcomes assuming each good is a normal good. Can we tell if the person will purchase more X? Can we tell if the person will buy more Y?

3. Do problem 2 over again, except that instead of the price of X falling to $2, the price of Y rises to $6.

4. a) For a demand curve Q(d) = 600 – 15*P, find the quantity demanded and total revenue paid for prices of $30, $25, $15, and $5.

b) In each case, reduce the price by $0.50 and calculate the new amount of total revenue. Calculate how much the total revenue changed in each case if price falls by that amount.

c) Calculate the elasticity of demand at each of the four original prices. Which price or prices should the firm NOT charge, and why?

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