A maximizing consumer is endowed with gh= 20, 5h= 20 and has preferences described by the linear function d = 45. Initially i" = 2, i!= 3. Now i!= 1. Provided an Indifference Curve Analysis Diagram to illustrate and quantify the endowment, the initial bundle, the Hicksian substitution effect, the ordinary income effect and the endowment income effect as bundles E, A, B, C and D. Use arrows to clearly indicate the SE, Ordinary IE, Endowment IE and Total Effect Her SE moves her from x =________ to x = Her Ordinary IE moves her from x = to x Her Endowment IE moves her from x = ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
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- Pls help with thsi question Consider an Individual who buys films (F) and books (B) with the following utility function:?(?, ?) = 5? + 2?This individual also has the following incomes (m) and prices (pF and pB):? = $50, ?f= $5, ?b= $10Given the above:1) Draw the utility functions for utility levels of 10 and 20. Draw these with films on the x-axis and books on the y-axis. 2) What is the MRS for these utility functions? Assume that films remain on the x-axis andbooks remain on the y-axis. 3) What is the consumption bundle that delivers the highest level of utility that is alsoaffordable?Sanjana loves to read books(B) and likes to watch movies(M) as well. She derives double the satisfaction from reading a book than watching a movie. Her utility function is as followsU(B, M) = 2B + MWhere B and M are the number of books and movies respectively.a. Explain the shape of the indifference curve using diagrams. b. The income available with her is INR60. And price of movie ticket is INR 10 and that of a book is INR 15. Will she spend her entire budget and why? What will be her consumption, explain why?A 2015 report by the music industry estimated the revenue lost to the industry every yearfrom illegal downloading. In this problem we will derive some of the estimates that may havegone into their calculation (approximately).First, start with the individual consumer’s problem. Suppose a typical consumer has a yearlyentertainment budget of I that they can allocate between music downloads (D) and otherforms of entertainment (E). Consumer preferences are characterized by a utility functionU(D, E). a.) Write an expression for the consumer’s budget constraint as a function of their entertainment budget and the prices of music downloads (Pd ) and other entertainment (Pe). (b) Write the consumer’s constrained optimization problem in Lagrangian form. (Note: Youdo not need to solve it or derive first order conditions.)
- 2. A consumer has a utility fuinction given by a) Derive an expression for the two marginal utilities: MU (x1, 22) and MU2 (21, r2). Since AMRS = -YU use these marginal utilities to derive a simple expression for the MRS (r1, 22). b) Optimal choice on the part of the consumer implies MI RS = -. Suppose M 20, p1 = p2 = 1. Show the optimal choice in this case on a well-labelled graph of the budget set. Include an indifference curve consistent with these preferences. c) Now keep income at 20, and pi = 1, but set p2 - 2. Show the optimal choice in this case on a well-labelled graplh of the budget set. Inclnde an indifference curve consistent with these preferences.Under the ordinal theory, a consumer is expected to rank his or her scale of preference from the least to the most satisfying. From this knowledge, describe the assumptions of the ordinal utility theory how do t the consumer attains equilibrium under the indifference curve approach use the idea of microeconmics ,show how the demand curve is derived under the cardinal theory approach(a) Suppose we have preferences U(X, Y) = 10X²/³ Y¹/3, Create a table and graph/sketch the indifference curve through the bundle X = 30 and Y = 30.< (b) The Marginal Rate of Substitution is MRSxy=-2Y/X. For the bundle (X= 30, Y = 30), calculate and then interpret what the value of the MRS means.< (c) Cobb-Douglas preferences are strictly convex. What does this imply about the MRS as we move along the indifference curve? Explain/discuss (you may want to draw a picture). < (d) What are the two conditions (equations) that identify the optimum given these preferences and the consumer's budget constraint? Sketch this in a figure and explain.< (e)_From (d) we can show that optimal demands are: X=½ M/PX and Y = ½ M/Px. (you do not have to derive these, just use the equations I have given you.) Calculate optimal demands (X*, Y*) and utility if Px = 10, Px= 5 and income M = 1200. < (f)_Suppose Px falls to Px = 8 but Py and M are unchanged (Px = 5 and M = 1200). Calculate the new optimal demands…
- 1. Consider a utility maximizer with complete, transitive, and monotonic preferences. Sup- pose you have data on the pairs of choices made by the consumer at different times. The bundles comprising these pairs of choices are y = (x1, x2) and z = (21, 22). For each of the scenarios given below, make use of the axiomatic properties of the preferences to say whether y is >, <, 3, E, or incomparable t z. (a) y =(2,4) and z = (1, 4) (b) y =(0,4) and w 3 z, where w =(3, 6) (c) y =(2,4) and z = (6, 3)1. For each of the following scaling functions for a von Neumann-Morgenstern utility func- tion, determine the Marginal Rate of Substitution between X1 and X2 and the equation for an indifference curve through the consumption bundle (100,100) (solve for X2 on the left hand side of the equation). State 1 is the bad outcome that occurs with probability 0.2 and State 2 the good outcome that occurs with probability 0.8. Graph these indif- ference curves and comment on what you see. Is a consumer with these preferences risk averse, risk neutral, or risk loving? (a) V(X) = InX (b) V(X)= VX (c) V(X)= X (d) V(X)= X²Exercise 3 An individual lives two periods, 0 and 1. The income is 14,000 in period 0 and 5,000 in period 1. The individual's marginal utility is: K- Co in period 0 and d8(K – C1) in period 1, where C is the consumption in period 0, C1 the consumption in period 1 and d a discount rate. K is a constant (higher than the consumption in each period). Suppose that the person can save or borrow from the bank from period 0 to period 1 with a 25% interest rate. Set the discount rate & to 0.8. a) How much will the individual consume in the two periods? How much will she save? b) A National Insurance scheme (pension system) is established. The individual must pay 4,500 in period 0 and receives the same amount with interests in addition to her income in period 1. What will the consumption and savings be in the two periods if the National Insurance scheme uses the same interest rate as the bank?
- J 4 a. Define an Indifference Curve (IC).During any year, I can consume any amount that doesnot exceed my current wealth. If I consume c dollars duringa year, I earn ca units of happiness. By the beginning of thenext year, the previous year’s ending wealth grows by afactor k.a Formulate a recursion that can be used to maximizetotal utility earned during the next T years. Assume Ioriginally have w0 dollars.b Let ft(w) be the maximum utility earned during years t, t 1, . . . , T, given that I have w dollars at the be-ginning of year t; and ct(w) be the amount that should be consumed during year t to attain ft(w). By workingbackward, show that for appropriately chosen constantsat and bt,ft(w) btwa and ct(w) atwInterpret these results.Draw the indifference curve for someone decidinghow to allocate time between work and leisure.Suppose the wage increases. Is it possible that theperson’s consumption would fall? Is this plausible?Discuss. (Hint: Think about income and substitutioneffects.)