Assume a firm has the following short-run production function: q (L) = L+ 10L²-L3 If this firm is going to maximize profits in the short-run by producing a strictly positive level of output (q > 0), what is the lowest level of labor (L) they would employ? Minimum L

Q: Consider the production functions of three different Firms utilizing inputs labor (L) and  capital…

A: X = KL2 – L3; Y = 10K1.5L0.5; Z = K0.5L0.5

Q: Suppose a firm produces according to the production function Q=3K/3L/3 and faces a wage rate of $5…

A: The Production function Q = 3K1/3L1/3 Wage rate(w) = $5 Rental rate of capital(r) = $2 Output price…

Q: 2wrQ Suppose the long-run cost function is given by: C(w,r. Q) = What would be the conditional…

A: Answer: Given, Long-run total cost function: Cw,r,Q=2wrQw+r The equation for conditional demand for…

Q: 1. Consider a firm with Total Output function (Production Function) given by Q = 6L2 – 0.4L3, where…

A: NOTE: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…

Q: Consider the following short-run production function (where L = variable input, Q = output):Q = 6L2…

A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: A soap manufacturer has the production function q = LK² and faces a wage rate of $45 and rental rate…

A: We know,  q=LK2  w=$45 r-$90

Q: A firm faces the production function q = L²K³. Capital is fixed in the short-run at K = 1. Each unit…

A: q=14L2K3 Capital is fixed at K=1 Cost of labor=w Cost of capital=r

Q: The production function for a firm is q=−0.6L^3+18L^2 K+10L where q is the amount of output, L is…

A: The average product of labor is the total product of labor divided by the number of units of labor…

Q: Suppose the short-run production function is q = 11L². Suppose that the wage rate is $112 per unit…

A: The firm produces goods and services which would result in the minimisation of the cost.with the…

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: Consider the following short-run production function (where L = variable input, Q = output): Q = 6L…

A: Marginal product is the ratio of change in input to change in output. The average product is the…

Q: Given the following production function. If the price of the output is $100. What is the Marginal…

A: Answer; Marginal Revenue product of labor = Marginal Product of labor * Price of output produced by…

Q: Demonstrate that the production functions satisfy the conditions for monotonically increasing,…

A: Given information An economy producing 2 goods Corn and potatoes Production function for Corn…

Q: y= f(x1,x2)=x1ax2b Derive the equation for an isoquant curve.   If a=b=0.5 , the price of factor 1…

A: y = x1ax2b x2b = y / (x1a) x2 = [y / (x1a)](1/b)

Q: A firm has a short-run production function as Q = 50 L + 6 L2 – 0.5 L3 Where Q = Quantity of…

A: The short-run is the time period where at least one factor is fixed and others are variable. In…

Q: 1. A firm's production function is Q = 50L – 0.01L , where L denotes the size of the workforce. Find…

A: Given information:  Q = 50L - 0.01L2 The formula for MPL = aQ/aL 50 - 0.02L2-1 50 - 0.02L

Q: Q7-9. Suppose the hourly wage is $2, the price of each unit of capital is $4, and the price of…

A: Production function: F(K,E) = (KE)1/2 Where K is capital  E is labor -------- Hourly wage rate is…

Q: Assume a firm has the following short-run production function: q (L) = L+10L² - L³ If this firm is…

A: The production function provides the relationship between the factor inputs used in production and…

Q: Suppose that the production function of the firm is: Q = 100L1/2.K1/2 K= 100, P = $1, w = $30 and r…

A: Given, Q = 100L12K12K= 100 P = $1 w = $30r = $40.

Q: A widget manufacturer has a production function of the form q = 6L + 10K . If the wage rate (w) is…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Question #3 Suppose a firm's short-run cost function is given by the following expression: C(q) = 10…

A: Given: The firm's short-run cost function is:  Cq = 10 + 14q - 6q2 + q3 To Find: Assuming this…

Q: The law of diminishing marginal returns will occur in a competitive firm as labor input is varied…

A: According to the law of diminishing marginal return, marginal return of labor will decline if we…

Q: Question 8: Profit maximization A firm's short-run production function is given with Q(K,L) = L02K².…

A: a)   An isoquant is the set of all the combinations of inputs which yield the same level of output.…

Q: > Consider this total product function with a single variable input, labor (L) per day: TPL = Q(L) =…

A: Total Product refers to the sum of all the products whether goods or services that are produced by a…

Q: Suppose a short-run production function is described as Q=30L-0.05L^2 where L is the number of…

A: Suppose, each unit of output has a marginal revenue of $5 and marginal cost of $40, the labours…

Q: Consider the long-run cost minimisation problem, with L on the horizontal axis and K on the vertical…

A: A firm will minimise its cost at a point where marginal rate of technical substitution is equal to…

Q: For a competitive firm; production function, market price and unit costs for capital and labour are…

A: Given, Q(K,L) = K1/2L1/4 and p = 8, r =0.1 , w = 10 Input demand for Labor L = f (w,r,p) Input…

Q: Consider a firm with Total Output function (Production Function) given by Q = 6L2 – 0.4L3, where L…

A: Answer given in image below...

Q: Suppose that the production function of the firm is: Q = 100L1/2.K1/2  K= 100, P = $1, w =$50. and…

A: Answer: Given, Production function: Q=100L12K12 K=100 P=$1 w=$50 r=$40 Calculation: To find the…

Q: In the short run, a tool manufacturer has a fixed amount of capital with labor as its primary…

A: A production function illustrates the relationship between the inputs used and the output produced…

Q: c) Give a formal definition of increasing, decreasing, and constant returns to sale, and determine…

A: Increasing Returns to Scale Increasing our inputs by m increases our output by more than m. Constant…

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: ONLY ANSWER C & D   Consider a firm with Total Output function (Production Function) given by Q =…

A: please find the answer below.

Q: Consider a purely competitive firm that has two variable inputs L (labor hour) and K (machine) for…

A: We maximize the production function subject to the cost constraints. Cost=C=wL+rk Maximize:…

Q: A firm is currently producing 500 units of output daily by employing 60 units of labor daily at a…

A: marginal rate of technical substitution is the rate at which one factor of production can be…

Q: Given the Production function for Mwaba & Mutale Enterprises as follows: Q = f (k,l) = 300k 2l2 - k…

A: Introduction Production is said to be the transformation of input into output. Total product is the…

Q: Consider Delta, a price-taking single-output, single input firm with the following production…

A: Non decreasing returns to scale implies that the rate of change of output w.r.t to the rate of…

Q: Suppose that the production function of the firm is: Q = 100L1/2 . K1/2 K= 100, P = $1, w = $50 and…

A: production function is referred to the relation of the number of inputs which a firm uses with its…

Q: Assume a firm has the following short-run production function: q(L) = L+6L2-1/2L3 If this firm is…

A: Answer in step 2

Q: 3. Suppose a firm has the following production function q = LK4. Let the unit price of capital be 1…

A: Setup a Lagrange function to maximize production subject to cost constraint. Price of labor is w and…

Q: The production function for global electronics is Q=2k^0.5 L^0.5 Assume that the capital stock is…

A: Profit=Total Revenue(TR)- Total cost (TC) Total Revenue=Price×QuantityTotal Cost=wLAs K=9,…

Q: Suppose the long-run cost function is given by: C(w.r,Q) = (w+r) 2wrQ What would be the conditional…

A: The conditional demand for an input like capital and labor (K* and L*) signifies the level of the…

Q: Assume there is a linear isoquant where the input combination  K = 10, L = 0 produces Q = 100.…

A: The isoquant would result in the downward sloping curve which would result in various combinations…

Q: For the production function q = f(K, L) the ratio of the percentage change on with PK is called…

A: cobb douglas production function:- Q=ALαKβ in the cobb douglas production function, we have…

Q: Suppose you have following production function for your firm :q = 2x,"x, where x, > 0, x, >0 and a ±…

A: Production function:  q = λx1ax21-a   ..........(1) Input price x1 = w and x2 = r The marginal…

Q: Assume labor (L) is the only variable input used in the production process, a firm’s production…

A: Production refers to the process in which the output is produced using the factors of productions.…

Q: Assume that a fırm has the following short-run production function: q (L) = 2L² – L³ The firm must…

A: Given, Short-run production function = q(L) = 2L2 - 1/2L3 Wages (w) per unit of labor (L) = 40…

Q: The firm's production function is given as: Q (L,K) = 2L + 30K. The costs of Labor (L) and Capital…

A: We have Q(L, K)=2L+30K            ... (1) w=$20 and r=$2 Desired output=1000