d) Solve numerically for quantity produced and labor and capital demanded when v = 1, w = 1. e) What happens to quantity produced and labor and capital demanded when v increases to 4?
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Just part (d) and (e)
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- Question A Suppose the short-run production function is q = 1L0.5. If the marginal cost of producing the 10th unit is $8, what is the wage per unit of labor? Question B A consumer has the utility function U(q1,q2) = q10.5 + q2Assume p2 = 1 and Y = 100. What is the equivalent variation of a price increase for good 1 from 1 to 4?Suppose that Marie produces milk q using her own labor l and cattle k using the production functionq = f(k, l) = k2/3ℓ1/3Although Marie does not need to pay anyone to use either input, the opportunity costs of labor and cattle are w = 1 and v = 16, respectively, and P is the price of milk. a) Suppose that Marie’s stock of cattle is fixed at k0 = 8. Set up her short run cost minimization problem and find her labor demand ℓ(q) and cost function SC(q). b) Find Marie’s short run marginal cost SMC(q) and average cost SAC(q) functions and find the quantity at which short run average cost is minimized. c) Set up Marie’s short run profit maximization problem and find her short run supply curve q(P).A competitive firm’s production function is given by y= f(x1,x2)= 4x11/2 + 10x21/2 a) The price of factor 1 is 1, the price of factor 2 is 1, and the price of output is 2. Find the profit-maximizing quantities of x1 and x2? What is the profit-maximizing quantity of output? b) Redo part (a), this time by first deriving the firm’s factor demand functions and the supply function, and then substituting the prices in these functions.
- To maximize profit, a price taker will expand its output as long as the sale of additional units adds more to revenues (marginal revenues) than to costs (marginal costs). Therefore, the profit-maximizing price taker will produce the output level at which marginal revenue (and price) equals marginal cost. In a price-taker market, if a business produces efficiently (i.e., that is, where marginal revenues = marginal costs), the firm will be able to make at least a normal profit. True of False. ExplainSuppose a typical (representative) corn farm has a short run production technology which results in the outcome of U-shaped Average Variable Cost (AVC), Average Total Cost (ATC), and Marginal Cost (MC). Further, suppose this firm sells its product in a market where the price of the good is determined by the interaction of market Demand and Supply. Because an individual firm is very small compared to the rest of the market, we treat the market price as the price given to the firm, and the individual firm cannot impact that price. assume we are in the Short Run for this firm. In graphing, put $ on the vertical axis and lower-case q (firm output) on the horizontal axis. Start with the AFC0, AVC0, ATC0, and MC0 curves . show shifts in any of the cost curves, reflecting the higher cost of land (keeping in mind that this higher cost is independent of how much or how little corn is actually produced) and labeling the changed cost curves with a subscript 1. On the graph with $ on the…Exercise: A firm produces output according to the following production function: q = A K1/4 L1/4 The price of capital is labeled r and the price of labor is labeled w and there is a set-up cost labeled F. Solve the cost minimization problem and do the following: If A = 6, r = 4, w =25 and the firm wants to produce q = 36, Determine this firm’s demand for capital K*. Group of answer choices a)15 b)45 c)90 d)60
- A purely competitive firm has a single variable input L (labor), with the wage rate W0 per period. Its fixed inputs cost the firm a total of F dollars per period. The price of the product is P0. (a) write the production function, revenue function, cost function, and profit function of the firm. (b) What is the first-order condition for profit maximization? Give this condition an economic interpretation. (c) What economic circumstances would ensure that profit is maximized rather thatn minimized?In each of the following four cases, MRPL and MRPC refer to the marginal revenue products of labor and capital, respectively, and PL and PC refer to their prices. Indicate in each case whether the conditions are consistent with maximum profits for the firm. If not, state which resource(s) should be used in larger amounts and which resource(s) should be used in smaller amounts. a. MRPL = $8; PL = $4; MRPC = $8; PC = $4. b. MRPL = $10; PL = $12; MRPC = $14; PC = $9. c. MRPL = $6; PL = $6; MRPC = $12; PC = $12. d. MRPL = $22; PL = $26; MRPC = $16; PC = $19.Suppose the utility function of a person consuming two commodities X and Y with income Birr 600 is given by U =2xy. If the per unit price of X is Birr 20 and per unit price of Y is Birr 40. a) Calculate the utility maximizing level of consumption of X1 and X2. b) Find the MRSX, Y at the optimum.If the production function of a firm is given by Q=,and the input prices are r = Birr 8 per unit and w = Birr 2 per unit,
- Only need the (d) , thank you , do fast Suppose that Marie produces milk q using her own labor l and cattle k using the production function q = f(k, l) = (k^(2/3))*(ℓ^(1/3)) Although Marie does not need to pay anyone to use either input, the opportunity costs of labor and cattle are w = 1 and v = 16, respectively, and P is the price of milk. (a) Suppose that Marie’s stock of cattle is fixed at k0 = 8. Set up her short run cost minimization problem and find her labor demand ℓ(q) and cost function SC(q). (b) Find Marie’s short run marginal cost SMC(q) and average cost SAC(q) functions and find the quantity at which short run average cost is minimized. (c) Set up Marie’s short run profit maximization problem and find her short run supply curve q(P). d) Now consider Marie’s problem in the long run, where her stock of cattle may vary. Set up her long run cost minimization problem and find her labor ℓ c (q) and capital k c (q) demands and cost function C(q). (e) Set up Marie’s long run…11 7. Suppose that for some reason we were interested in studying solutions to the following problem: A firm produces a single output y from N inputs x = (x1 , • • • , xN) . The firm is given a certain budget that it can spend on inputs, and the firm produces as much output as it can given that budget. Letting B be the budget and supposing the firm is described by a production function f (x ) and that the firm is competitive and faces factor prices w, we can define y* (w, B) = max{f (x) :w ·x ::.; B}. Devise a theory concerning this problem in the spirit of the results we have given concerning partial derivatives of y* and solutions to the problem just posed.Suppose the productivity of capital and labor are as shown in the accompanying table. The output of these resources sells in a purely competitive market for $1 per unit. Both capital and labor are hired under purely competitive conditions at $3 and $1, respectively. a. What is the least-cost combination of labor and capital the firm should employ in producing 80 units of output? Explain. b. What is the profit-maximizing combination of labor and capital the firm should use? Explain. What is the resulting level of output? What is the economic profit? Is this the least costly way of producing the profit maximizing output?