An individual has utility function for X and Y of the form U(X,Y)= X + Y and Py expenditure function as a function of prices px, py and utility level Ū is E(Pæ‚Py,Ū) = PxŪ Ū E(Px, Py, Ū) Px E(Pa, Py, ‚Ū) = (Px +Py) Ū ○ E(Pæ, Py,Ū) = PÂŪ || - The
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- Clarice has a utility function: U(Y) = 1000 - (100/Y), where Y is her income. clarice has just graduated from college and has a career choice for her first job of either working as a teacher and earning $40,000 or trying to become a theatre lighting director and earning $70,000 (if there is growth in the demand for theatre) or $20,000 (if there isn't growth in the demand for theatre). there is a 50% probability of growth. a consulting firm guarantees Clarice that it already knows whether there will be growth in the demand for theatre next year. what is the maximum amount Clarice should be willing to pay for this information?Consider an individual whose preferences are represented by the utility function U(x1,x2) = min {3x1+x2 , x1+3x2}. For this individual, Plot the indifference curve giving a utility level of 6. Calculate her MRS at consumption bundle (x1,x2), does MRS depend on the value of (x1,x2)? Calculate her optimal consumption bundle when she has an income of 24, and P1=1, P2=2. Calculate her optimal consumption bundle when she has an income of 24, and P1=1, P2=4. Calculate the income and substitution effects resulting from the change in price of Good 2 (on the level of Good 2 consumption!) Calculate her demand function X1* (P1, P2,m) Calculate her own price, cross price, and income elasticities at X1*(1, 2, 24) and at X1*(1, 4, 24). Based on these, can you say the goods 1 and 2 are (gross, or Marshallian) complements or substitutes?Show the derivation of the individual demand function for a utility maximizer consumer and explain the common properties for the points on the fuction which you show.
- 33. Suppose MRSx,y = MUx/MUy = 0.1(a) If the consumer substitutes 10 units of X for one unit of Y, then the utility remainsunchanged(b) Regardless of prices, the consumer will only consume Y(c) If the consumer substitutes 1 unit of Y for 0.1 unit of X, then the utility remainsunchanged(d) Regardless of prices, the consumer will only consume X1. What is the relationship between pS/pC and pC /pB? What feature of the utility function is responsible for these ratios?2. Now suppose that the moment before the above prices are elicited, the subject gets $10, which does not become part of her reference point. Again calculate the three prices pS, pB, and pC. What is the relationship between pS/pC and pC /pB? Why? 3. In some actual experiments, subjects were not given money, and pS/PC was found to be about 2, and PC/pB was found to be about 1. Write down a utility function that can produce these ratios.Economists use "indifference curves" to indicate individuals' preferences. These curves are parallel to each other and do not intersect. Which of the following statements is true? A) The further away an indifference curve is from the origin at (0,0), the lower is the individual's happiness. B) On a downward-sloping indifference curve, the points lower down (towards the right-hand-side) on the curve are preferred by the individual. C) The closer an indifference curve is to the origin at (0,0), the higher is the individual's happiness. D) The further away an indifference curve is from the origin at (0,0), the higher is the individual's happiness.
- Q2. Amanda receives satisfaction from consumption C and leisure L. Her utility function is given by U(C, L) = L x C. a. Define indifference curve. [5 points] b. Name 2 properties of indifference curves. [5 points]Find the indifference curves corresponding to the following utility functions at different utility levels, three by three, and the MRSDerive utility maximisation of a consumer using the tool of indifference curve analysis
- Given the Utility Function is U = X0.7Y0.3 and Budget is taka 300. The original price was (Px, Py) = (2, 2) and the new price is (Px’, Py) = (4, 2). (a) Draw an angle curve for X by using the above information [Labelling is must] (b) Calculate the value of Compensation variation (CV) and Equivalent variation (EV)?Let u(x) be a utility function that represents the preferences of a household. We say that the function v(x) is a monotonic transformation of u if f(·) is a strictly increasing function and v(x) = f(u(x)). (a) Show that if v(x) is a monotonic transformation of u, it represents the same preferences. (b) Can you explain why taking a monotonic transformation of a utility function does not change the marginal rate of substitution? (c) What kind of preferences are represented by a utility function of the form U(x1,x2) = ? What about the function U(x1,x2) = 13x1+13x2?A consumer is having a monotonic preference. What can you say about his preference on these bundles (10,10) (10,9) (9,9)
