3 Question 3 A firm with production function F(K, L) = K√L currently has 2 units of capital and faces a market price of p = 3 and a rental rate of r = 1. Give a range of possible wage rates, w, for which this firm would have negative short run profits.
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- Are there fixed costs in the lung-run? Explain briefly.What is the relationship between marginal product and marginal cost? (Hint: Look at the curves.) Why do you suppose that is? Is this relationship the same in the long run as in the short run?Automobile manufacturing is an industry subject to significant economies of scale. Suppose there are four domestic auto manufacturers, but the demand for domestic autos is no more than 2.5 times the quantity produced at the bottom of the long-run average cost curve. What do you expect will happen to the domestic auto industry in the long run?
- 1-a Suppose you have following production function for your firm : q = Ax;“x, where x, > 0, x, > 0 and a ± 0, a0. The price of input x, is w>0 and the price of x, is r > 0. a) Compute the marginal products of xi and x2. b) Using Lagrange method, write down cost minimization problem and first order conditions. c) Determine the conditional factor demands and cost function of the firm, x1* x2* and C* as a function of w, r, q and 2.A chair manufacturer hires its assembly-line labor for $20 an hour and calculates that the rental cost of its machinery is $10 per hour. Suppose that a chair can be produced using 4 hours of labor or machinery in any combination. If the firm is currently using 2 hours of labor for every two hours of machine time, is it minimizing its cost of production? If so, why? If not, how can it improve the situation? The firm O A. is not currently minimizing its cost of production because the ratio of the marginal product of labor to the marginal product capital is equal to the ratio of the wage rate to the rental cost. O B. is currently minimizing its cost of production because its marginal rate of technical substitution less than the ratio of input prices. C. is not currently minimizing its cost of production because the marginal product of labor divided by the wage is less than the marginal product of capital divided by the rental cost. O D. is currently minimizing its cost of production…2. A firm has the following Cobb-Douglas production function: q = LªK!-a, where 0 < a <1 is a parameter. Suppose that in the short run K = 1. The rental rate of a unit of K is $10, and the wage rate of a unit of L is $20. (a) Derive the marginal cost of the firm (expressed in terms of a and q). (b) Derive the average variable cost of the firm (expressed in terms of a and q). (c) Derive the cost function of the firm.
- A chair manufacturer hires its assembly-line labor for $5 an hour and calculates that the rental cost of its machinery is $10 per hour. Suppose that a chair can be produced using 4 hours of labor or machinery in any combination. If the firm is currently using 2 hours of labor for every two hours of machine time, is it minimizing its cost of production? If so, why? If not, how can it improve the situation? The firm O A. is currently minimizing its cost of production because its marginal rate of technical substitution is greater than the ratio of input prices. O B. is not currently minimizing its cost of production because the ratio of the marginal product of labor to the marginal product of capital is less than the ratio of the wage rate to the rental cost. O C. is currently minimizing its cost of production because its marginal rate of technical substitution equals the ratio of input prices. O D. is not currently minimizing its cost of production because the marginal product of labor…Tripod Store has been so successful in Paris that it wants to set up a new operation in Nantes. Their long-run production func tion is Q = K2/3L1/3 The rental rate of capital is $12 and the wage is $10. The market price of cameras is $6, and Tripod expects to sell 1000 per month. a. What is the opti mal allocation of capital and labor (per month) for the new loc ation? b. In add ition to the price of labor and capital, Tripod will have to pay $8000 per month in fixed costs—rent, insurance, etc. Does this change your answer to part (A) above?2. Suppose the hourly wage is $10 and the price of each unit of capital is $25. The price of output is constant at $50 per unit. The production function is f(E, K) = E'/²K'/2. (a) Write a firm's short-run profit maximization problem. (b) Find a firm's marginal product of labor MP(E). (c) Find the second order condition and derive the labor demand function (i.e. An increase in wage decreases the number of workers hired). (d) If the current capital is fixed at 1,600 units, how much labor should the firm employ in the short run? (e) How much profit will the firm earn?
- 1. A shortGHH run production function of a competitive firm is given by Y=6L^(2/3)where Y represents the units of output while L is the labour required. If P = 3 and W =6. (ii). What is the firms profit at the optimal level?The expansion path of a firm gives five different quantities of output such as 10,20,30,40 and 50 units; and the price of labor is $25 and the price of capital is $100 per unit. The table shows the long-run costs of the firm at given quantities of output. Q L K LTC( $) LAC( $) LMC ($) 10 64 20 3600 360 360 20 120 40 7000 350 340 30 200 58 10800 360 380 40 288 80 15200 380 440 50 440 90 20000 400 480 a. With the help of graph, analyze the properties of LAC and LMC b. Interpret and evaluate the numerical and graphical data and illustrate the relationship between LAC and LMCK Suppose that a firm's production function is q=5x in the short run, where there are fixed costs of $1,000, and x is the variable input whose cost is $625 per unit. What is the total cost of producing a level of output q? In other words, identify the total cost function C(q). The total cost of producing ya level of output q is A. C(q)= 1,000. OB. OC. OD. OE C(q)= 1,000+ C(q)= 1,000+ C(q) = 1,000+ 625q² C(q)= 25 q² 25 625q² 25 0.5 q B Dollars per unit of output 2000- 1800- 1600- 1400- 1200- 1000- 800- 600 400- 200- a 12 14 10 Quantity nchack 18 (1) Incorrect