Draw the isocost. draw this initial isocost. Show the slope of the isocost Suppose that w = $10,r= $5 and your budget as the manager of a firm is C= $110. In the graph below Next, suppose that when you pay a $10 fee, you join a program that gives you the following benefits: a) get a "buy-one-get-one free" promotion on labor; b) it decreases the price of capital by 20%; and it gives you 3 free capital. In the same graph below, please draw the new isocost (so the graph should have both the old and new isocost).
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- Show the profit function is convex in (p, c). Provide an intuitionfor this result. hint: Consider (p, c), (p', c') and (pα, cα) = α(p, c) + (1 −α)(p', c'). Let w, w' and wα denote the corresponding factor demands. What do you know about the relation between (the size of) pf(w)−cw and pf(wα)−cwα, as required by the definition of profit-maximizing?Q2: Let a consumer’s daily hours of work is denoted by H, and hours of leisure by L. Consumer has no other source of income except wages for hours worked. She consumes what she earns each day. Her utility function is U(C, N) = ln(C) + 3 ln(N) Where C stands for the dollar amount of her consumption. Now answer following questions (a) Suppose the wage rate is 50Rs. per hour. Write down the consumer’s utility function and budget constraint with C and H as the choice variables. (b) How many hours will she choose to work, and what will be the resulting utility?The manager of Dixie Furniture Company estimates that the daily output of her factory (in thousands of dollars) Q is given by Q = 2x1/4y3/4 where x is the amount spent on labor and y is the amount spent on capital (both measured in thousands of dollars). (a) Find the daily output of the factory if $81,000 is spent on labor and $256,000 is spent on capital each day. $ (b) Suppose that the output of the factory is to be maintained at the level found in part (a). By how much should the amount spent on capital be changed if the amount on labor is increased by $1,000? (Use the differential to calculate the answer. Round your answer to the nearest cent.) $ What is the MRTS? (Round your answer to the nearest cent.) $ per thousand dollars
- With the use of an example, briefly explain the main difference between the ex-ante and the ex-post opportunity cost of capital. Why does this matter for the evaluation of an investment decision? In what ways can managers utilise the distinction between ex-ante and ex-post opportunity cost of capital when deciding on the firm’s strategy?Consider a representative consumer with preferences over consumption e and leisure I given by u(e,l) = 1/4 * ln(c) + 3/4 * ln(l) Assume that the price of consumption is normalized to p = 1 and the consumer has h = 24 hours of total time available to divide between work and leisure. The consumer's wage per hour of work is w = 24 The consumer also receives dividend (profit) income of pi = 39 and pays lump-sum taxes of T = 7 (a) Write out the consumer's budget equation, and draw a graph of the budget constraint. (b) Solve for the optimal decisions e and 1. How many hours per day is the consumer working? (c) Suppose the consumer's wage decreases to w = 16 Solve for the new optimal choices of c and I". Relative to the solution in part (b), do consumption, leisure, and hours worked increase, decrease, or stay the same? Give an intuitive explanation for why these changes occur. (d) When the wage changes in part e, determine whether the consumer experiences an income effect, a substitution…21. Let U=x 2 +y 2 is the utility function of a worker who has 10 hours that to be allocatedbetween labour supply (L) and leisure (x). Let y is a consumption good whose price is 1.Wage rate (w) is Rs 1 and non-wage income is 20. Find out L.a) 10 b) 0 c) 5 d) 8 e) none 22. On the basis of the above question, hen w=0 and non-wage income is 40, find out L.a) 10 b) 0 c) 5 d) 8 e) none
- Consider 5 workers who care about their consumption and continuous job satisfaction J.Their preferences are described by the utility function U(C,J) = 2C + J. There are 5 firms thatare producing the output using the production function Q(J,L) = L√20 − J1. What are the marginal rate of substitution between consumption and job satisfaction andthe marginal rate of transformation between wages and job satisfaction?2. What are the equilibrium levels of wage and job satisfaction?3. What is the slope of the wage-job satisfaction locus?Indicate whether the following statetment is true, false or uncertain and briefly explain why. Use formulas or diagram whenever necessary. Suppose that a firm uses capital, K and labor, L in order to produce output and that rental price of capital is v and wage rate of labor is w. If w decreases, then the demand for capital by the firm will decrease.6. If pMP1 >w1, then should the firm increase or decrease the amount of factor 1 in order to increase profits?
- 1 The consumption-leisure framework Suppose that the representative consumer has the following utility function over consumption (c) and labour (n): u(c, l) = ln c − A 1 + � n 1+� (1) where, as usual, c denotes consumption and n denotes the number of hours of labour the consumer chooses to work, The constants A and � are outside the control of the individual, but each is strictly positive. Suppose the budget constraint (in real terms) faced by the individual is given by: c = (1 − t) · w · n (2) where t is the labour tax rate, w is the real hourly wage rate, and n is the number of hours the individual works. Remember, as seen in class, n + l = 1 is always true. Using the static consumption-leisure framework, answer the questions that follow. 1. State the utility maximization problem, and state carefully the choice variables in the problem. [2] 2. Write the Lagrangian function for this problem. [2] 3. Using the Lagrangian function from above, derive the first order condition with respect…Consider an otherwise standard Arrow Debreu Equilibrium with some modifications. Suppose that households now are not allowed to own capital directly. Instead, firms own all of the initial capital stock ko and also make all future investments in capital. Households own all shares of the firms, and returns to the firms now include returns to capital. Make necessary changes to the firm's and the household's problems to fit the new arrangement, define the new equilibrium, and show that the equilibrium quantities and prices are same as before.Shelly’s preferences for consumption and leisure can be expressed as U(C, L) = (C - 200) * (L - 80) This utility function implies that Shelly’s marginal utility of leisure is C - 200 and her marginal utility of consumption is L - 80. There are 168 hours in the week available to split between work and leisure. Shelly earns $5 per hour after taxes. She also receives $320 worth of welfare benefits each week regardless of how much she works. a. Graph Shelly’s budget line. b. What is Shelly’s marginal rate of substitution when L = 100 and she is on her budget line? c. What is Shelly’s reservation wage? d. Find Shelly’s optimal amount of consumption and leisure.