2. Solve for the short-run profit maximization problem for f(x1, x2) = 2x1 + x2 and f(x1, x2) = min{2x1, x2}, holding x2 at 2, and taking real factor prices w₁ and w2 as given.
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- Solve for the short-run profit maximization problem for f(x1, x2) = 2x1 + x2 and f(x1, x2) = min{2x1, x2}, holding x2 at x2*, and taking real factor prices w₁ and w2 as given.An employer who employs m workers determines that they produce: units of that product daily. Total income (in dollars) is given by: 1) ¿What is the price, per unit, when there are 30 workers? 2) Determine the marginal revenue when there are 30 workers. 3) The product of marginal income corresponds to the rate of change of income with respect to the number of active employees, at a given moment. Determine the product of marginal revenue when m = 30Suppose a competitive firm operation under the following conditions: price of output is $20, the profit maximizing level of output is 32,000 units, and the total cost(full economic cost) of producing these 32,000 units is $600,000. The firm’s only fixed factor of production (capital) is a $1 million building and you would like to include the opportunity cost of this investment at the going interest rate of 5%. Should this firm close down immediately? What will it do in the long run?
- Making dresses is a labor-intensive process. Indeed, the production function of a dressmaking firm is well described by the equation Q = L − L2/(23*100), where Q denotes the number of dresses per week and L is the number of labor hours per week. The firm’s additional cost of hiring an extra hour of labor is about $5 per hour (wage plus fringe benefits). The firm faces the fixed selling price, P = $40. How much labor should the firm employ? (Round your answer to the nearest whole number.)QUESTION 2The total production of a good y is determined by the production function y = 3L2/3K1/3, where L is labour input and K capital input.The reward (factor prices) for labour and capital are, l = 27 en r = 2, respectively.The producer needs to produce 9000 units of good y.How much units of labour will he hire if he wants to miminize his total costs? 1587,4839,953000515,23A firm's production function is: q = 16L1/2K1/3 where q is the firm's hourly total product, L is the quantity of labor employed, and K is the quantity of capital employed. Assume that the quantity of capital employed is fixed at 125 units per hour. The labor market is perfectly competitive, and the current wage, w, is $10 per hour. The firm sells its product in a perfectly competitive market and the price is $5 per unit. a. What is the firm's value of marginal product of labor? b. What is the firm's profit maximizing quantity of labor?
- A firm's production function is: q= 10L1/2K1/4 where q is the firm's daily total product, L is the quantity of labor employed in hours, and K is the quantity of capital employed in units. Assume that the quantity of capital employed is fixed at 256 units. The labor market is perfectly competitive, and the current wage is $12 per hour. The firm sells its product in a perfectly competitive market and the price is $6 per unit. a. What is the firm's value of marginal product for labor? b. What is the firm's profit maximizing quantity of labor?Q29 Suppose a firm is employing labour (L) and capital (K) such that MPK/MPL = PK/PL. If the price of labour rises, the cost-minimising firm should then... a. Employ more labour and less capital because MPK/MPL > PK/PL. b. Employ more capital and less labour because MPK/MPL > PK/PL. c. Employ more capital and less labour because MPK/MPL < PK/PL. d. Do nothing. e. Employ more labour and less capital because MPK/MPL < PK/PL.10. If over the range of positive marginal product, the short-run total product of factor A in the production of X is given by the equation: X=aA +b A2 – A3 Where a, and b are positive constants, and if the average product of A is maximized when X=100, then the marginal product of A must be greater than the average product when X=50. True or False ?. Prove your answer.
- Explain Sraffa’s critique of the Marshallian industry supply curve based on diminishing returns under the general case. note: for example when it says that the industry accounts for a very small share of the total quantity of the fixed factorQuestion 5. A cost minimising firm has labour as its only input, but labour has two components, the number of workers, N, and hours per worker, h. Each worker hired incurs fixed costs (i.e. costs that do not vary with output), f, while the wage for “standard hours” (hours up to and including 40 hours per week) is w per hour. For hours above 40 the firm must pay its workers an overtime premium of 50 percent, i.e. 1.5w. a) Derive the firm’s isolabour function (the function showing combinations of N and h which generate the same overall employee-hours).b) Derive the firm’s isocost function (the function showing combinations of N and h which generate the same total cost of labour). [HINT: it will have two “segments”, one for less than 40 hours per week and one for more than 40 hours per week.] c) Sketch the isolabour and isocost functions (with N on the y-axis and h on the x-axis). [HINT: to be able to show the isocost curve and know its shape, it helps to find out how its slope changes…Making dresses is a labor-intensive process. Indeed, the production function of a dressmaking firm is well described by the equation Q = L − L2∕800, where Q denotes the number of dresses per week and L is the number of labor hours per week. The firm’s additional cost of hiring an extra hour of labor is about $20 per hour (wage plus fringe benefits). The firm faces the fixed selling price, P = $40. Over the next two years, labor costs are expected to be unchanged, but dress prices are expected to increase to $50. What effect will this have on the firm’s optimal output? A- Increase B- Decrease C- No Effect
