uppose a worker’s utility is U = C 1/2L1/2. C is expenditures on goods, L is hours of leisure. He has a total of 16 hours for work and leisure, and the market wage is $10 per hour. Solve for his optimal C and L (assume V=0
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Suppose a worker’s utility is U = C 1/2L1/2. C is expenditures on goods, L is hours of leisure. He has a total of 16 hours for work and leisure, and the market wage is $10 per hour. Solve for his optimal C and L (assume V=0
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- The utility that Elena receives by consuming food F and clothing C is given by U(F,C) = FC + F. Food costs £1 per unit, and clothing costs £2 per unit. Elena's income is£22. MUF = C+1 and MUc = F.(i) Define the term Marginal Rate of Substitution (MRS). (ii) Find the utility maximizing values of C and F for the numerical values given above(Hint: You can assume interior solution). (ili) Now suppose that price of C and Elena's income remain unchanged at £2 per unitand £22, respectively, while the price of F varies. Find the equation of the demand forF as a function of the unit price of F (PF).John works in a shoe factory. He can work as many hours per day as he wishes at a wage rate w. Let C be the amount of dollars he spends on consumer goods and R. be the number of hours of leisure that he chooses. John's preferences are represented by U(C, R) = CR utility function Question 2 Part a John earns $8 an hour and has 18 hours per day to devote to labor or leisure, and he has $16 of nonlabor income per day. Draw John's indifference curves, budget constraints and solve for his optimal consumption and leisure choices.What is the optimal number of work hours for the student whose utility function for other goods (X) and leisure (L) is U (C,L) = CL, and who has $50 of nonlabor income per week and the possibility to work at $5 per hour. Assume that after studying for class & other activities, the student has only 50 hours per week remaining to choose between work and leisure.
- The utility of a consumer derives from consuming the two goods X and Y can be assumed to be determined by the utility functionU(X,Y)= 4X03Y05. If good X costs 10 birr a unit and good Y costs 15 birr a unit and the consumer's income is 120 birr. What combination of X and Y that will maximize utility?Aisha is considering how to allocate the next 6 hours of her free time. She could choose between leisure (L) and helping her neighbour with the house chores. If she decides to help her neighbour, she is going to get paid at £25 per hour, which she can then spend on her favourite pizza (P). Suppose the price of pizza is £12.50. Aisha's preferences for leisure and pizza are given by the following utility function: U(L, P) = 3L + P. (MUL = 3, MUp = 1). a) Write down Aisha's budget equation and draw the corresponding budget line. Clearly label the axes and calculate the coordinates of the points of intersection of the budget line with each axis. b) Calculate Aisha's marginal rate of substitution between leisure and pizza. Explain the concept of MRS and interpret the figure obtained. c) Find Aisha's optimal consumption bundle, both algebraically and graphically. Explain your reasoning. d) Would Aisha's optimal choice change if she could get a discount on her pizza purchases so that each…An individuals utility function is given by U = 340x1 + 960x2 + 2x, x2 - 2x – x3/2, when the weekly amount of leisure is x = 132 and earned income is x2 = 760 answer the following 1. The marginal utility of x is 2. The marginal utility of x2 is 3. Use the small increments formula to estimate the change in the utility when x decreases by 1 and x2 increases by 4. The change= 4. Does the law of diminishing marginal utility hold? 5. The MRCS at a given values is Enter non-integer numerical values as decimals to at least 3 decimal places. Note: you must use a . and not, for a decimal point.
- Aisha is considering how to allocate the next 6 hours of her free time. She could choose between leisure (L) and helping her neighbour with the house chores. If she decides to help her neighbour, she is going to get paid at £25 per hour, which she can then spend on her favourite pizza (P). Suppose the price of pizza is £12.50. Aisha's preferences for leisure and pizza are given by the following utility function: U (L, P) = 3L + P. (MUL = 3, MUp = 1). a) Write down Aisha's budget equation and draw the corresponding budget line. Clearly label the axes and calculate the coordinates of the points of intersection of the budget line with each axis. d) Would Aisha's optimal choice change if she could get a discount on her pizza purchases so that each pizza would cost £5? Explain. e) Would Aisha's optimal choice change (as compared to c), if she could get a discount on her pizza purchases so that each additional pizza beyond the first two, cost £5? (In other words, the first two pizzas need to…Consider a person with the utility function U (C, L) = (1 − α) log C + α log L, where L is leisure time and C is consumption of other goods measured in dollars. The person has V dollars of non-labor income and a wage of w. There are T hours available for either working or leisure. 1. Write down the person’s budget constraint. Draw a graph representing this constraint, taking care to label the axes and key points. 2. What are the person’s marginal utilities for consumption and leisure? What is her marginal rate of substitution between leisure and consumption in terms of C, L, and α? 3. Write down a condition involving the person’s marginal rate of substitution that characterizes her optimal choice. Represent this condition graphically and interpret in words. 4. Solve for the person’s optimal choices of leisure and consumption, L ∗ and C ∗ , in terms of T, V , w, and α. 5. How does L ∗ change as you increase wage w and non-labor income V ? 6. How does C ∗ change as you increase wage…A shady raccoon strands you on a deserted island with nothing but tree branches (B) andcherries (C). Suppose your utility over branches and cherries is given byU(B,C) = B1/4C3/4 a.) Calculate your marginal rate of substitution as a function of B and C.
- Calculate the marginal rate of substitution (MRS12) for the following utility function: U (91, 92) = 67√√9₁ +0.4(92)4 1 What is the value of MRS12 at bundle (7,4)? Please round your final answer to two decimal places if necessary. 0.12Terry’s utility function over leisure (L) and other goods (Y ) is U(L, Y ) = Y + LY. The associated marginal utilities are MUY = 1 + L and MUL = Y. He purchases other goods at a price of $1, out of the income he earns from working. Show that, no matter what Terry’s wage rate, the optimal number of hours of leisure that he consumes is always the same. (a) What is the number of hours he would like to have for leisure? Determine the MRS of leisure for labour (b) Draw a leisure-influenced labor curveTerry’s utility function over leisure (L) and other goods (Y) is U (L, Y) = Y + LY. The associated marginal utilities are MUY = 1 + L and MUL = Y. He purchases other goods at a price of $1, out of the income he earns from working. Show that, no matter what Terry’s wage rate, the optimal number of hours of leisure that he consumes is always the same. (a) What is the number of hours he would like to have for leisure? (b) Determine the MRS of leisure for labour (c) Draw a leisure-influenced labor curve