For which of the following utility functions indifference curves are strictly convex? If more than one option is correct choose (e). (Assume only non-negative quantities Select one: O a. U(r1, r)-7x4( O b. U(11,2) = min(2.r,3) Oc. U(T,2) = 5r + 10r2 o d. U(r1,12) - 8r1 + a O e. More than one of the above

For which of the following utility functions indifference curves are strictly convex? If more than one option is correct choose (e). (Assume only non-negative quantities Select one: O a. U(r1, r)-7x4( O b. U(11,2) = min(2.r,3) Oc. U(T,2) = 5r + 10r2 o d. U(r1,12) - 8r1 + a O e. More than one of the above

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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D E B 04 What does point D on this graph represent? O An optimal choice O A choice on the budget constraint O An impossible choice given the income O A choice that would result in income left over
(a) Suppose we have preferences U(X, Y) = min [X, 3Y]. Graph/sketch the indifference curve through the bundle (X = 30, Y = 30). What is the utility of (30, 30) and explain why the indifference curves look the way they do. (b) What does the Marginal Rate of Substitution tell us about preferences? < (c) Why is the Marginal Rate of Substitution not applicable in this example? < (d) What do we mean by a composite good? What does this composite good look like with these preferences? Show and explain.< (e) State the consumer's maximization problem and express this in words.< (f) Now let Px = 10, Px= 20 and income M = 2000. Find optimal X*, Y*, and the resulting Utility (U*). Show your work. < (g) Now let Py = 15. How does optimal consumption (X*.Y*) and utility (U*) change relative to (e)? Explain in simple terms and show in a diagram.<
O let ,U= H (2, Xs)- (t,t 2X3) be a whility funstion da total derivative to ferive MRS O let û (a, Xs)x,+22,, be pns Hher utility funtn Doer "û and u Explain describe the same
Suppose that the following utility function is given U(X,Y) = x/3y1/2, Which of the following is correct? O We have convex preferences since Law of diminishing Marginal Rate of Substitution holds and indifference curves are bowed inward towards the origin We have convex preferences since Law of diminishing Marginal Utility holds and indifference curves are bowed outward from the origin O We have convex preferences since Law of diminishing Marginal Rate of Substitution fails to hold and indifference curves are bowed inward towards the origin O We have non-convex preferences since Law of diminishing Marginal Rate of Substitution holds and indifference curves are bowed inward towards the origin
Question 21 A consumer chooses an optimal consumption point where the O marginal rate of substitution is maximized O slope of the indifference curve exceeds the slope of the budget constraint by the greatest amount O ratio of the marginal utilities equals the ratio of the prices O All of the above are correct
The consumer choice is not restricted to the choice of consumptiongoods. In fact, it can apply to all our decisions that involve trade-offs. Suppose Mary has awage per hour of 10 euros. With her earned income she consumes. That isC=wH per day.She also decides how many hours to work of take leisure time each day.H=24-N, whereHis work and N is leisure. Her utility is given by （picture） Solve for the optimal decision of labor/leisure. Plot the budget constraint and the indif-ferent curve. What is the labor supply function?
Problem 2 Suppose that John's preferences over meat (M) and vegetables (V) are represented by the following utility function U(M,V) = a ln(M) + (1 − a) ln(V) where 0 < a < 1. ¹No claim of realism is made for the numbers in this example. 1 (a) Write down the Lagrangian for John's optimization problem. (Recall that John max- imizes utility given an income, I, and prices på and på for the goods.) (b) Solve for John's optimal consumption bundle (M*, V*) (as a function of income and prices) using the Lagrangian method. = (c) Suppose a = . Suppose also that John has income I = 1 and pv 2. What is the value of John's optimal happens if John's income doubles to I = 400? 200 and faces prices p consumption bundle? What =
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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c and d please