1. Consider the utility function U(X)=X1.X2. a. Check whether the above function is strictly quasi concave....
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
1. Consider the utility function U(X)=X1.X2. a. Check whether the above function is strictly quasi concave. b. Solve the U-Max problem for the consumer and find X1 and X2 in terms of P1, P2 and M. Make sure you check the second order condition (SOC). c. What does the result in (a) imply for the SOC of utility maximization problem? Prove your claim. d. Derive the indirect utility function. e. Is V (P. M) homogeneous in P and M. Interpret your result? f. Find XI and X2, using Roy's identity and explain your result intuitively. g. Derive the expenditure function, e(P,U) by solving V (P, M) for M. h. Using Sheppard's lemma, find h1 and h2 and explain your result intuitively. i. Verify your results in (h) by solving the expenditure minimization problem. Make sure you check the SOC. j. Verify your result in (g) by finding the expenditure function, using h1 and h2. k. Check whether e (P, U) is concave in P. 1. Discuss briefly, comparing X(P.M) and h(P,U). m. Assume P1-P2-$2 and M-$200. Find the numerical values for the optimum XI, X2 and the maximum utility. n. Assume P1-P2-$2 and the numerical value for the maximum utility in (m). Find the numerical values for h1 and h2, using the results in (h) or (i). Compare your results in (m) and (n) and interpret. o. p. Suppose P1 increases to $4 and P2 stays the same. Find the income and substitution effects of this price change. q. Explain the result in (p), using indifference curves and X(P.M) and h(P,U) demand functions. r. Find the new budget to protect the same utility. s. Find the amount of subvention needed to keep the consumer at the same utility level t. Find the MRS for the (50,50) consumption point using utility function. u. Assume P1-P2-$2. Find the MRS. 1. Consider the utility function U(X)=X1.X2. a. Check whether the above function is strictly quasi concave. b. Solve the U-Max problem for the consumer and find X1 and X2 in terms of P1, P2 and M. Make sure you check the second order condition (SOC). c. What does the result in (a) imply for the SOC of utility maximization problem? Prove your claim. d. Derive the indirect utility function. e. Is V (P. M) homogeneous in P and M. Interpret your result? f. Find XI and X2, using Roy's identity and explain your result intuitively. g. Derive the expenditure function, e(P,U) by solving V (P, M) for M. h. Using Sheppard's lemma, find h1 and h2 and explain your result intuitively. i. Verify your results in (h) by solving the expenditure minimization problem. Make sure you check the SOC. j. Verify your result in (g) by finding the expenditure function, using h1 and h2. k. Check whether e (P, U) is concave in P. 1. Discuss briefly, comparing X(P.M) and h(P,U). m. Assume P1-P2-$2 and M-$200. Find the numerical values for the optimum XI, X2 and the maximum utility. n. Assume P1-P2-$2 and the numerical value for the maximum utility in (m). Find the numerical values for h1 and h2, using the results in (h) or (i). Compare your results in (m) and (n) and interpret. o. p. Suppose P1 increases to $4 and P2 stays the same. Find the income and substitution effects of this price change. q. Explain the result in (p), using indifference curves and X(P.M) and h(P,U) demand functions. r. Find the new budget to protect the same utility. s. Find the amount of subvention needed to keep the consumer at the same utility level t. Find the MRS for the (50,50) consumption point using utility function. u. Assume P1-P2-$2. Find the MRS.
Expert Answer:
Answer rating: 100% (QA)
It appears that you have a series of questions related to consumer utility maximization demand functions and related concepts in microeconomics Ill address each question step by step a To check whethe... View the full answer
Related Book For
Posted Date:
Students also viewed these economics questions
-
Suppose that the person with the above utility function is struck by lightning. He survives, except now his utility function is u = 1 log(x1 1) + 2 log(x2 2). Will his consumption decisions change...
-
The following additional information is available for the Dr. Ivan and Irene Incisor family from Chapters 1-5. Ivan's grandfather died and left a portfolio of municipal bonds. In 2012, they pay Ivan...
-
What approximate value should come in place of the question mark ?' in the following question? (1800 + v? x 29.99) 15.02 = 144
-
The following information relates to the business of Biddulph, for the year ended 31 March 20*8: Stock at 1 April 20*7 4,560; stock at 31 March 20*8 5,050; purchases for the year 47,800; sales for...
-
In a lecture demonstration, laser light is used to illuminate two slits separated by 0.5 mm, and the interference pattern is observed on a screen 5 m away. The distance on the screen from the...
-
In your opinion, what are the two or three things most important to monitor and control in order to ensure your project will deliver value to your client?
-
Consider the following cash flow profile and assume MARR is 10 percent/year. a. What does Descartes' rule of signs tell us about the IRR(s) of this project? b. What does Norstrom's criterion tell us...
-
Given the following network, determine the first activity to be crashed by the following priority rules: (a) Shortest task first (b) Minimum slack first (c) Most critical followers (d) Mostsuccessors...
-
Imagine that your friend Mary has normal metabolism, but that her brother John has galactosemia. Mary and John's parents, Patricia and Les, are unaffected, although their maternal grandmother, Jean,...
-
Based in China, Lenovo is one of the largest computer brands in the world. Several years ago Lenovo purchased IBM's PC business and now sells more computers to retail customers and businesses than...
-
SUBJECT: ACCOUNTING The owner got some goods costing P450 but priced to sell for P500 to be given as a gift to a friend. What is the journal entry based on perpetual system
-
The risk that a bond issuer may not pay on its bonds is known as Blank______.
-
6. The following ciphertext PULCL YTHRL LEJLW APVUZ HULEJ LWAPV UKPZW YVCLZ AOLYBSL was obtained using a Vigenre cipher with a keyword of length p. Here is the frequency table for the letters in this...
-
List the five ways companies can departmentalize. Then, give an example of each of the five.
-
discuss some potiential impact on marketing research activities.
-
3. (10 points) Please label the name of the corresponding coding technique used in the figure. 00 00011
-
Use the accompanying a. Find the quartiles. b. Find the interquartile range. c. Identify any outliers. 56 64 63 56 58 55 58 65 55 62 56 63 64 54 83 data set to complete the following actions. a. Find...
-
A 2500-lbm car moving at 15 mi/h is accelerated at a constant rate of 15 ft/s 2 up to a speed of 50 mi/h. Calculate force and total time required?
-
If the resultant force of the two tugboats is required to be directed towards the positive x-axis, and F R is to be a minimum, determine the magnitude of F R and F B and the angle . FA= 2 kN 30 B
-
Determine the coordinate direction angles , , of force F, so that the moment of F about O is zero. 0.4 m A, -0.5 m- 0.3 m
-
The bearing consists of rollers, symmetrically confined within the housing. The bottom one is subjected to a 125-N force at its contact A due to the load on the shaft. Determine the normal reactions...
-
The group \(\mathrm{D}_{3}\) in Schoenflies notation (32 in international notation, which is read "three-two"; see Table 5.1 ) consists of the proper (those not reflections or inversions) covering...
-
Derive the two-dimensional matrix representation Tic)=(2) Tin)=(3) Tex)=(37) (69) T(c2b)= 1 TO)-(71) 10-(11) TO=(9) = for the group D3, using the basis (e1, e2) defined in the following figure.
-
Prove that the matrix representation of \(\mathrm{D}_{3}\) worked out in Problem 5.6 is irreducible. Data from Problem 5.6 Derive the two-dimensional matrix representation Tic)=(2) Tin)=(3)...
Study smarter with the SolutionInn App