1 Consider a consumer who consumes only two goods, 21 and z2. His utility function is u (21, 22) = In z1 + 2.where In represents the natural logarithm.1.a Derive the consumer's MRS of good 1 for good 2 using calculus to calculate his marginal utility from zand his marginal utility from z2.1.b If the price of z1 is $2 per unit and the price of z2 is $4 per unit, and the consumer's income is $100,What is the equation of this consumer's budget line?1.c What are the optimal consumption choices, z and z5, for this consumer? Show your work.

Utility function is given as:- U(z1,z2) = lnz1+z2 Price of z1 = $2 Price of z2 = $4 Income = 100

Answered: 1 Consider a consumer who consumes only…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

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2. Ping receives a weekly allowance to purchase soda (x) and juice (y) at school. His preferences over these two goods can be represented by the utility function U(x,y) =0.5x+ 5lny where x represents the number of cans of soda and y represents the number of juice boxes. a) Given his preferences find his Marshallian demand functions for soda (x) and juice (y). b) Suppose that the price of a can of soda is $1.5 and that Ping has $30 to spend on soda and juice. Write Ping's demand curve for juice (y). Illustrate his demand curve. c) Suppose that the price of a box of juice is $1 (the price of soda and income remain $1.5 and $30, resp.). Use your demand functions to find his best bundle. In an indifference curve diagram illustrate his best bundle at these prices. For the remainder of the question assume that Ping's allowance (income) rises to $36 per week and the prices of the two goods are unchanged at Px= $1.5 and Py= $1. d) Use your demand functions to find his new best bundle. e)…
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QUESTION 1 For the utility function U = Qx0.50Qy(1-0.50) and the budget 122 = 8Qx + 14Qy find the CHANGE in optimal consumption of Y if the price of Xincreases by a factor of 1.7. Please enter your response as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 1.2, 1.14 = 1.1).
. Consider an economy with the following features. . There are 100 identical consumers that derive utility from consuming three different goods: software, computers, and good m. • Each consumer decision utility function is given by U (c, s) = 4c¹/4g¹/4+m, where e denotes the amount of computers that she consumes, s denotes the amount of software that she consumes, and m denotes the amount of good m that she consumes. cand s must be non-negative, but m can take any real value. • Computers are produced by 20 identical competitive firms with a total cost function given by 10c². • Software is produced by 40 identical competitive firms with a total cost function given by 20s². . QUESTION 1: What are the equilibrium prices for software and comput- ers in equilibrium?
Suppose an individual is currently spending all of their income on a bundle of books and pizza, but they are not sure whether the bundle maximizes their utility. Assume the individual has a strictly diminishing marginal rate of substitution over these two goods. At their current bundle of books and pizza, the individual's marginal utility from consuming books is 6 utils and their marginal utility from consuming pizza is 3 utils. If the current price of a book is $12 and the price of a pizza is $7, which of the following statements must be true: A. The individual can increase their utility by consuming more books and less pizza B. The individual is maximizing their utility C. The individual can increase their utility by consuming more pizza and fewer books
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5. Jonas purchases only two goods, starfruit (S) and kiwi (K). He has an income of $60 and can buy starfruit at $2 per pound and kiwi at $3 per pound. His utility function is U(S,K)=3S+4K. That is, his (constant) marginal utility for starfruit is 3 and his marginal utility for kiwi is 4. What bundle of starfruit and kiwi should he purchase to maximize his utility? Why?
B.3 Marie has preferences over two goods, cake q₁ and bread q2. She chooses quantities to consume so as to best satisfy these preferences subject to the budget constraint p1q1 + P292 y where p₁ and P2 are prices and y is total budget. Suppose that Marie's preferences are represented by utility function u(q1, 92) = 91 + In (bq1 +92) where b≥ 0 is a preference parameter. Assume that p1/bp2 ≥ y/ (P1 - bp2) ≥ 1. (a) Show that Marie's indifference curves are downward sloping and that her weakly preferred sets are convex for all possible values of b. (b) Show that her Marshallian demand for cake gi is Y fi (y, P1, P2) 1 P1-bp2 and find her Marshallian demand for bread, f2 (y, P1, P2). Discuss the shape of Engel curves for the two goods. (c) Explain why Marshallian demand curves for normal goods slope down. Are there any values of b for which either cake or bread could be a Giffen good for Marie? Discuss. (d) Find the form of the indirect utility function and expenditure function and hence…
Assume, as in Exercise 22.1, that a consumer has utility function F or fruit and chocolate. Determine the consumer's demand functions q1(P1, P2, M) and q2(P1, P2, M). Determine also It* in terms of P1, P2 and M. Find the indirect utility function and show that It* = 8Vj8M. Suppose, as before, that fruit costs $1 per unit and chocolate $2 per unit. If the income is raised from $36 to $36.5, determine the precise value of the resulting change in the indirect utility function. Show that this is approximately equal to (O.5)λ*, where λ* is evaluated at P1 = 1,P2 = 2 and M = 36. Exercise 22.1 A consumer purchases quantities of two commodities, fruit and chocolate, each month. The consumer's utility function is For a bundle (X1, X2) of X1 units of fruit and X2 units of chocolate. The consumer has a total of $49 to spend on fruit and chocolate each month. Fruit cost $1 per unit and chocolate costs $2 per unit. How many units of each should the consumer buy…
1. Suppose you are considering to make a decent holiday dinner. In this year, to be creative, you are thinking to put Copper River Salmon from Alaska (fillet) and fresh Atlantic Lobsters from Maine as entrée on the table. Use the information given, to finish the questions below. (1) The table following provides you total utility (U) and marginal (MU) from consuming Salmon and Lobster. Suppose your total utility of Salmon consumption (U1) is a function of the units (Q as pound or lbs.) of salmon consumed, as U1 =. =/400Q. Similarly, your total utility of Lobster (U2) has the form as units (Q as lbs.) of lobster consumed, which is U2 = /36Q + 40. Now fill the empty spots in the table using the information given. Total utility and marginal utility of Salmon and Lobster. Copper River Salmon Atlantic Lobster Q (Ibs.) U1 MU1 U2 MU2 1 20.00 20.00 8.72 8.72 2 3 4. 6. 7 8 10 (2) With a certain amount of budget, you are going to purchase both Salmon and Lobsters. To maximize your total…
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