A plant's production function is Q = 2KL. For this production function, MPx = 2L and MPL = 2K. The price of labor, w, is $4 and of capital, r, is $6 per unit. a) In the short run, the plant's capital is fixed at K = 5. Find the amount of labor it must employ to produce Q = 300 units of output. b) How much money is the firm losing by not having the ability to choose its level of capital optimally? Hint: Solve the long run cost minimization problem (where the firm can choose its level of both capital and labor) and compare the cost of the solution with the cost of the inputs used in the answer to part a.
Q: Suppose a firm uses two inputs: capital, K, and labour, L. The profit function is π(K, L, p, w, r)…
A: To find the rate of change in the maximum profit we differentiate the maximum profit function with…
Q: Suppose the hourly wage is $20 and the price of each unit of capital is $2. The price of output is…
A: The firm maximizes profit by hiring the number of workers at a point where MPE = w/p
Q: The total cost function of a firm is given by: C = q(wy{v)! Where q is total output, W and V are…
A:
Q: A firm in a competitive marketplace employs 10 workers at a wage rate of $20 per hour, and 10 units…
A: Cost Minimization Producers utilize cost minimization as a fundamental guideline to identify what…
Q: Suppose the marginal productivity of capital is 50 units of output and the marginal productivity of…
A: In financial matters, the marginal product of capital (MPK) is the extra creation that a firm…
Q: Suppose that a firm’s production function is q =L0.5K0.5. This means that the marginal rate of…
A: The production function shows the relationship between the factors of production to be used and the…
Q: Suppose Julia currently consumes positive amounts of cheesecake and coffee and her marginal rate of…
A: We know at the optimal MRS = Price Ratio
Q: A short run production function of a competitive firm is given by Y=6L^(2/3) where Y represents the…
A: Given, Y = 6 L23 P = 3 W = 6
Q: A firm uses labor (L) and capital (K) to produce rocking chairs (Q) with the following production…
A: Short-run: - it is a short time period in which some factors of production are variable and some are…
Q: Question 1 The total cost function of a firm is given by: 2 C = q(W){cv) Where q is total output, W…
A: Note: Since a student has asked more than one question, we are going to ask the first question as…
Q: A firm produces output that can be sold at a price of $10. The production function is given by Q =…
A: The production function is given below.
Q: Suppose the firm is hiring labor and capital and that the ratio of marginal products of the two…
A: Marginal product: It refers to the input, i.e. labor which is defined as an extra output that…
Q: Suppose that a firm's production function is given by Q = KL. If capital is fixed at 1 unit in the…
A: The labor market is the market that is determined by employment and wages. The labor demand curve…
Q: Suppose the production function for high quality brandy is given by : Q = √KL Where q is the output…
A: Given : Q = 10 √L L = Q 2/100 Part a) Cost function : C = Rk + wl K = 100 , R = 10 and w = 5 C =…
Q: A firm uses labor (L) and capital (K) to produce rocking chairs (Q) with the following production…
A: In the short run capital is fixed and cannot be changed.
Q: Charlie's Umbrellas has a production function given by Q = L^0.5K^0.5. The wage (W) is $80 per day…
A: Q = L0.5K0.5 Wage (W) = $80 Rental per unit of capital (R) = $5
Q: A widget manufacturer has a production function of the form q = L? K² . If the wage rate (w) is $4…
A: Since you have posted multiple parts questions, we will solve the first three parts for you. If you…
Q: When a firm uses K units of capital and L units of labor, it can produce Q units of output with the…
A: Production function measures the relationship between the units of output produced by using the…
Q: Suppose a firm has the following widget production function: q=2K/₁2, the wage rate, w = $20 and the…
A: Given Production function: q=2K1/2L1/2 .... (1) w=$20 and r=$180 In short-run K is…
Q: Which of the following is incorrect? As we take the partial derivative of the long-run cots function…
A: Long Run Cost is the total expenditure incurred in the production process for the production of…
Q: Consider the following shortrun production function: (Q=100L- L*L), where Q is the output level and…
A: Given Short-run production function: Q = 100L - L*L We can write this as Q = 100L - L² Price of…
Q: Given the production function y= f(x1,x2)=x11/3x21/3. The amount of x2 is equal to 216 in the short…
A: Given, y= f(x1,x2)=x11/3x21/3 Amount of x2 = 216
Q: Q = L1/2 K1/2 They have 16 units of capital (which is fixed in the short-run). The unit cost of…
A: The production function refers to the functional relationship between input and output, which…
Q: A firm produces output with capital and labor. Suppose currently the marginal product of labor is 28…
A: Answer to the question is as follows:
Q: The production function shows: a. The level of output as a function of the quantity of inputs.…
A: The markets are considered to be place where the meeting, and interaction of the buyers of various…
Q: Suppose that a firm’s production function is q =10L0.5K0.5 (i.e. q = 10√L√K). The cost of a unit…
A: Production function: q = 10L0.5K0.5 ---------- Cost of a unit of labor =20 => w =20 ----------…
Q: Miguel and Jake run a paper company. Each week they need to produce 1,000 reams of paper to ship to…
A: Cost is minimized at the point where ratio of marginal product of inputs is equal to price ratio of…
Q: Suppose a firm has a production function Q = 10/KL %3D so that 5/K MPL VI 5VL VK MPK The firm uses 9…
A: Cost = wL + rK We substitute everything given: Q=60, K=9 60 = 10(9)0.5(L)0.5 6 = 3(L)0.5 22 = L So L…
Q: A firm produces output y using two factors of production (Inputs), Labour L and capital K. The…
A: PRODUCTION FUNCTION -: It refers to…
Q: A production function for a good Q uses inputs of labor (L) and capital (K) and takes the form Q=LK.…
A: Cost The number of goods and services necessary to produce or manufacture is referred to as the…
Q: A firm has the following production function: q = L - K Assume the firm must pay each unit of labor…
A: In the short run, capital is fixed but in the long run all inputs are variable.In the long run, cost…
Q: Which of the following represents the optimal combination of Capital and Labor under the goal of…
A: The marginal rate of technical substitution is the rate at which one factor must decrease when an…
Q: A competitive firm produces its output, y according to the production function: y = F(K, L), where K…
A: The short-run profit function is equal to the revenue minus the total cost. The short-run supply…
Q: A company has a production function Q = (K)0.5 + L. For this production function MP, = 1 and MPK =…
A: Marginal product of labor is the additional unit of labor required to produce an extra unit of…
Q: A firm employs labor and capital by paying $40 per unit of labor employed and $200 per hour to rent…
A: Production function is convex at the first then after the inflexion point becomes concave. An…
Q: A competitive firm produces output using three fixed inputs and one variable input. The firm’s…
A: A competitive firm minimizes cost by employing the number of input where its marginal product is…
Q: Consider a firm with the production function q = L}K* The firm faces a wage rate of w = 20 and a…
A: The given production function is a ‘Cobb-Douglas’ function where the producer uses both labor(L) and…
Q: To produce a recorded DVD, a firm uses one blank disk D and the services of a recording machine M…
A: Given information Production function Q = min{D, M} Here 1 DVD is produced by using 1 blank disk…
Q: A firm’s production function is Q = L1/2 K1/2 They have 16 units of capital (which is fixed in the…
A: Given Q =L1/2K1/2 ...... (1) In short-run K = 16 (fixed) Cost of labour =2 and cost of capital =…
Q: Show your work whenever possible. A firm has the following production function. Q=K.√L the rent…
A: In the production of goods and services, various factors of production or inputs are used in…
Q: The production function of producing an item is given by 3K Q = 744 VK – where K is the capital…
A: Marginal product is determined by the change in total output as one additional input is used in the…
Q: A short run production function of a competitive firm is given by Y=6L^(2/3) where Y represents the…
A: The production function is defined as the express the relationship between the productive factors…
Q: A firm has a production function given by Q AL" K# and per unit prices of capital (K) and labour (L)…
A: given, Production function Q = ALαKβ Wages = w…
Q: For a short run production function q=10lnL if L=5 and wage 3, more workers will be hired if the…
A: more workers will be hired if the price at which the output can be sold is more than 1.5
Q: Joe's coffee shop has the production function, q= 4k0.5 L0.5. If the price of labor, L, is 5 and the…
A: q= 4k0.5 L0.5 PL = 5 PK = 20 q=200
Q: Suppose the marginal productivity of capital is 50 units of output and the marginal productivity of…
A: In financial matters, the marginal product of capital (MPK) is the extra creation that a firm…
Q: A firm faces the following production function: y(k, 1) = √k + √l. The output price is equal to 6,…
A: The firm is at optimum when it hires the number of input at a level where marginal product of the…
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
- X and X2 are the two factors used in production A firm's production function: fcx₁, x₂) = max {x₁, X₂} the price of X, is W₁=8, and the price of X₂ is W₂=10 The firm paproduce 100 total units of output, what is the total cost?Production Functions and Cost Functions in the short run and in the long run Consider the production function Q=KL. The firm needs to produce 64 units of output. The price of capital is R=$16 and the price of labor is W=$4 a. In the short run, the firm's capital is fixed at K=16. How much labor will it use? What is its short run total cost? Hint: Solve it for a generic Q and plug Q=64 only at the very end b. Find the firm's short run total cost, average total cost, and marginal cost curves. Hint: If you are trying to find cost curves, Q is unknown. c. Set up a Lagrangian to find the firm's optimal inputs in.A firm's production function is q = 26x^0.33y^0.67, where x and y are the amounts of factors x and y that the firm uses as inputs. If the firm is minimizing unit costs and if the price of factor x is 6 times the price of factor y, the ratio in which the firm will use factors x and y is closest to. A. x/y = 0.08 B. x/y = 0.25 C. x/y = 0.5 D. x/y = 2.4
- Consider a production function of two inputs, labor and capital given by Q=LK. Let w =5 and r = 1, where w is the price per unit of labor and r is the price per unit of capital. a) Suppose that the firm is required to produce Q units of output. Show how the cost-minimizing quantity of labor depends on the quantity Q? b) If the firm is operating in the short run, with K fixed at 10 units, calculate the short-run total cost of producing 100 units of output?A firm faces a production function given byq = √klwhere q is the output, k is the firm’s amount of capital equipment and ? is the amount of labour-time employed.(a) In the short run, the amount of capital equipment is fixed at k = 100. The rental rate for k is v = $1, and the wage rate for l is w = $2.Calculate the firm’s short-run average cost (SAC) and short-run marginal cost (SMC) functions. Graph the SAC and the SMC curves for the firm. (b) Where does the SMC curve intersect the SAC curve? Explain why the SMC curve will always intersect the SAC curve at its lowest point.(c) Calculate the long-run total cost of production. For w = $2, v = $1, graph the long-run total cost curve. Show that this is an envelope for the short-run curves computed in part (a).a) A firm operates according to the following production function: q(K,L)=100 KS LOS. The price of capital is r=$15/unit and the price of labor is w=$60 per unit. The firm currently operates with KSR-100 units of capital and wants to produce qs 4000 units of output. How much labor does the firm need to hire and what is the total cost of producing the 4000 units?
- A firm has the following production function: q = KL, where q is output, K is capital and L is labor. The price of a unit of capital is $1,000 and the price of a unit of labor is $500. The total cost includes the cost of capital and labor, as well as an additional $200 per unit of output for raw materials. The firm currently runs a single factory with 5 units of capital. Assume that capital is fixed in the short run. (a) How much does it cost to produce q units of output (in the short-run)? [The answer I expect is a particular function of q.] (b) Will the firm produce or shut down in the short run if the price of a unit of output is $300? Explain in at most one sentence.Suppose a firm producing wood burning stoves has the following production function Q(K, L) = 4K¹/2 [1/2 Where L, the labour, and K, the capital are the 2 inputs of production and Q the quantity of stoves. Assume the price of one unit of L is £1 and the price of one unit of K is £2. a) b) Assume that K=9 in the short run. Draw the production function and calculate the marginal products of L as L changes from L= 1 to L= 6. What does an isoquant curve show? Draw the graph of a production isoquant representing input combinations that will produce 8 units of output.1) Miguel and Jake run a paper company. Each week they need to produce 1,000 reams of paper to ship to their customers. The paper plant's long-run production function is: q = 4K L where q is the number of reams produced, Kis the quantity of capital rented, and L is the quantity of labor hired. For this production, MP, = and MP, = The weekly cost function for the paper plant is C= 10K +2L where C is the total weekly cost What ratio of capital to labor minimizes Miguel and Jake's total costs? (Hint: Find the Marginal Rate of Technical Substitution (MRTS) for capital and labor.) b. How much capital and labor will Miguel and Jake need to rent and hire in order to produce 1,000 reams of paper each week? How much will hiring these inputs cost them?
- A firm produces output according to a production function: Q = F(K,L) = min {4K,4L). a. How much output is produced when K= 2 and L = 1? unit(s) b. If the wage rate is $60 per hour and the rental rate on capital is $40 per hour, what is the cost-minimizing input mix for producing 8 units of output? Capital: Labor: c. How does your answer to part b change if the wage rate decreases to $40 per hour but the rental rate on capital remains at $40 per hour? O Capital decreases and labor increases. O It does not change. O Capital increases and labor decreases. O Capital and labor increase.Suppose that a firm’s production function is Q = 2L0.5 + 3K0.5. The cost of a unit of labour is R2 and the cost of a unit of capital is R1.a) Determine the firm's optimal ratio of labour to capital. b) Determine the level of capital and labour in the long run if the firm wants to apply a cost constraint of 396. Calculate the output of the firm. c) Graphically illustrate this using isoquant and isocost lines.A company has a production function Q = (K)0.5 + L. For this production function MP, = 1 and MPK = 0.5(K)-0.5. The firm faces w=$50 and r= $1. Keeping r =1, the price of labor, w, must fall to less than $ in order for the firm to use a positive amount of capital to produce 10 units, or the output Q must increase to over units for the firm to use a positive amount of capital, at w=$50.