Question 18 A firm has a long-run cost function, C(q) = 4q² + 100. In the long run, this firm will supply a positive amount of output, as long as the price is greater than Question 19 Assume that the production function for competitive firm is given by F(L) = 9L³,where Lis the number of units of labour used in the production process. Suppose that the cost per unit of labor is $3 and the price of output is $9 per unit, how many units of labor will the firm hire?

Question 18 A firm has a long-run cost function, C(q) = 4q² + 100. In the long run, this firm will supply a positive amount of output, as long as the price is greater than Question 19 Assume that the production function for competitive firm is given by F(L) = 9L³,where Lis the number of units of labour used in the production process. Suppose that the cost per unit of labor is $3 and the price of output is $9 per unit, how many units of labor will the firm hire?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter10: Cost Functions

Section: Chapter Questions

Problem 10.6P

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Assume that the production function for competitive firm is given by F(L)=9L1/3, where L is the number of units of labour used in the production process. Suppose that the cost per unit of labor is $3 and the price of output is $9 per unit, how many units of labor will the firm hire?
The Director of Jonat Enterprise hires labour (L) and rents capital equipment (K) in a competitive market to produce chocolate pellets. At the moment, the wage rate of labour is GH¢2 per hour and capital is rented at GHØ5 per hour. Also, the unit price of chocolate pellets is GH¢0.75 and total cost of production is GH¢1,000. Suppose the firm's production function (Q) follows a Cobb-Douglas specification given as: Q = 14K0.5 10.5 + 10 Page 3 of 4 Determine the optimal input usage and the maximum profit that Jonat Enterprise would obtain at the optimal input levels.
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Problem 5 Suppose that a firm has a production function f(K, L) = 12L¹/3 K¹/3 and that w and r are input prices and p is output price. The firm does not change those prices. a) Show that the firm's profit π is a concave function of (K, L). b) Find (K*, L*) that maximizes the profit, as a function of (w,r, p).
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7. A fast-food company in Hermanus has the following cost function: TC = 10 + 3K + 2L, where L is the number of labour hours and K is the number of machines they have to use. They have a production function of Q = 2KL, where Q represents the number of meals produced per day. The company has to make at least 75 meals every day. Using the Lagrangian method of production optimization, calculate the optimal number of labourers and machines needed to meet this quota. (6)
A competitive firm has a production function described as follows. Q = f(K, L) = 100K}L where K and L are levels of capital and labor in production respectively. (a) Find the optimal bundle of capital and labor to produce 400000 units of output, if the wage is w=$8 and the rental price of capital is r=$1. Also, find cost of producing 400000 units of output. (b) Suppose that in the short run this firm must use 40000 units of capital but can vary its amount of labor freely. How does optimal number of labor and cost of production changes? (consider prices and quantity given part a) (c) Write down a formula that describes the marginal product of labor in the short run as a function of the amount of labor used. (d) If the wage is w=$10 and the price of output is p=$2, how much labor will the firm demand in the short run? (e) Write down an equation for the firms short-run demand for labor as a function of w and p. (f) Write down an equation for the firms short-run cost function as a function…
The manager of Don Teeta Company Limited hires labour (L) and rents capital equipment (K) in a very competitive market. Currently, the wage rate of labour is GH¢2 per hour and capital is rented at GH¢5 per hour, the unit price of the product is GH¢0.75 and total cost of production is GH¢1,000. Suppose the firm's production function (Q) is as folows: Q = 14K05L05+ 10 Determine the optimal input usage and the maximum profit.
A firm has the production function F(L, K) = L^1/2 + K^1/2The price of labor is $10 and the price of capital is $15. The firm has a production goal of Q = 100 units ofoutput.a) Neatly specify this firm’s cost minimization problem, using the particulars associated with this problem.b) Give two equations that an interior solution satisfies, tailoring your equations to the particulars of thisproblem.c) Solve the two equations for the firm’s optimal choice. Show your work.
Problem 1 Hobbies Co is a firm that produces model trains in a perfectly competitive market. The production of each model train requires millilitres of paint (P), and grams of wood (W). Their production function is given by f(P,W)= min{6√P, 3W – 12}. (a) Draw the isoquant corresponding to q = 48 trains in a clearly labelled diagram where P is the horizontal axis and W is the vertical axis. Label two distinct input bundles (P, W) in the diagram which give q = 48. (b) Compute the marginal products of each input. (c) Does this production function exhibit constant returns to scale? Using the marginal products you have computed in the previous part, explain your answer in no more than 25 words. (d) Suppose that HobbiesCo wants to produce q trains when the price of paint is $72/mL and the price of wood is $18/g. Show that the minimum cost of such an undertaking is c(q) = 2q² +6q+72. (e) Suppose that the market price is p, and Hobbies Co will produce q units of trains. Using the cost function…
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 competitive firm has a production function described as follows. Weekly output is the square root of the minimum of the number of units of capital and the number of units of labor employed per week. Suppose that in the short run this firm must use 16 units of capital but can vary its amount of labor freely. (a) Write down a formula that describes the marginal product of labor in the short run as a function of the amount of labor used. (Be careful at the boundaries.) (b) If the wage is w=$1 and the price of output is p=$4, how much labor will the firm demand in the short run? (c) What if w=$1 and p=$10? (d) Write down an equation for the firms short-run demand for labor as a function of w and p.