Suppose there are 90 consumers in the market withtwo goods x and y. There are two types of individualsA and B. 60 of the consumers are type A and the 30of them are type B. Type A consumers have a utilityfunction of u(x, y) = x¹/³y¹/³ and each of themhas an income of mд. Type B consumers have autility function of u(x, y) = x²/³y¹/³ and each ofthem has an income of mp.3. Find the market demand for good x as a functionof incomes and prices.4. Find the market demand for good y as a functionof incomes and prices.5. Suppose price of good x is 2 and the price good yis 2. Further suppose mA = 60 and m³ =-120.Find the market demand for good x and good y atthe given prices and incomes.

Market demand refers to the total quantity of goods or services that consumers are willing and able…

Suppose there are 90 consumers in the market with two goods x and y. There are two types of individuals A and B. 60 of the consumers are type A and the 30 of them are type B. Type A consumers have a utility function of u(x, y) = x¹/³y¹/3 and each of them has an income of mд. Type B consumers have a utility function of u(x, y) = x²/3y¹/3 and each of

Suppose there are 90 consumers in the market with two goods x and y. There are two types of individuals A and B. 60 of the consumers are type A and the 30 of them are type B. Type A consumers have a utility function of u(x, y) = x¹/³y¹/3 and each of them has an income of mд. Type B consumers have a utility function of u(x, y) = x²/3y¹/3 and each of

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.12P

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solutions. Question 1 Calculating MRS for CD Utility Functions (a) If a consumer has a CD utility function 0.4 0.6 U(91,92) = 994926, calculate MRS1,2. (b) If a consumer has a CD utility function Ima kdown1 calculate MRS1,2. (c) If a consumer has an utility function noltan asd Tor sympy ,1-α U(91,92) = 91 92 llib et (.) orde (hing aid tol bholup U(91,92) = a ln(91) + (1 - a) ln(92), diw sonuanos of calculate MRS1,2. Is it the same as the result in the previous part? (Note: Recall that we discussed the concept of ordinal utility in class, which means only the order of utility matters, not its magnitude. In function is a monotone transformation on the CD utility function. Notice that In (qq) = a ln(9₁) + (1 - a) ln(92). This example verifies that a monotone transformation does not change *(S) sidshav the consumer's indifference curves.) wobei/ (d)
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A consumer’s preferences between goods x and y are representedby the utility function u(x, y) = 2min{x, y}+10. Suppose this consumer hasincome of $16, the price of good x is $3 and the price of good y is $1. Suppose the price of good x increases to $7 while the price of good y andthe consumer’s income stay constant. Calculate the magnitudes of the compensating and the equivalent variations. Explain what each measures.
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?
Pls help with thsi question I am stuck Given the image attatched: 1.Given the above Marginal Utilities and prices to form the optimality condition for utilitymaximization. According to this optimality condition, what must be the ratio of Films toBooks in an optimal consumption bundle? 2. Given your answer to Q9, what must be the household’s optimal consumption of F & Bgiven their income (m)? 3. Suppose that the price of Films changed from $2 to $4. What would need to happen tothe MRS according to the optimality condition in Q9 if the household wanted to keepmaximizing its utility?
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Suppose that the consumer maximizes his utilitysuch that the marginal utilities of goods X and Y are; MUx=80-16x MUy=60-2y Let Px=P4,Py=P2 and I=P80 Find the utility maximizing quantities X and Y
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Mylie’s total utility from singing the same song over andover is 50 utils after one repetition, 90 utils after tworepetitions, 70 utils after three repetitions, 20 utils afterfour repetitions, 250 utils after five repetitions, and 2200utils after six repetitions. Write down her marginal utilityfor each repetition. Once Mylie’s total utility beginsto decrease, does each additional singing of the songhurt more than the previous one or less than the previousone?
A consumer is making purchases of products Alpha and Beta such that the marginal utility of product Alpha is 63 and the marginal utility of product Beta is 40. The price of product Alpha is $9, and the price of product Beta is $5. The utility-maximizing rule suggests that, to stay within a given budget constraint, this consumer should Multiple Choice O O O increase consumption of product Beta and increase consumption of product Alpha. make no change in the consumption of Alpha or Beta. increase consumption of product Beta and decrease consumption of product Alpha. increase consumption of product Alpha and decrease consumption of product Beta.