Given a firm's cost function C = F(x) = ax² +bx + d:Find the firm's Average cost funetion (A(x) and Marginal cost function M(x). OIs C(x) more appropriatc as a long-run or short-run cost function? Explain.Determine whether the Marginal cost function is strictly monotonic for a> 0, b>0, andd> 0.Does this finction have an inverse for economically meaningful values of x? If yes, finddx/dM. If not, show/explain what restriction would be necessary for inverse to exist.a.b.c.d.

Answered: Given a firm's cost function C=F(x) =…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Assume a firm's short-run cost function is given by the following expression: C(q) = 2+q+q2 If the firm can sell each unit of their output at a price of p=9 dollars, what is the maximum profit the firm can earn in the short-run? a.) Maximum Profit = ? dollars
Subpart 1-3
The cost function of a firm is c(y) = 3y2 + 6y + 5. 1. Find the Average variable and Marginal Cost curves of the firm. 2. What is the quantity level where the average variable cost is minimized?
Catalina Films produces video shorts using digital editing equipment (K) and editors (L). The firm has the production function Q(K, L)=KxL, where Q is the hours of edited footage. The wage is $25, and the rental rate of capital is $50. The firm wants to produce 3,000 units of output at the lowest possible cost. a) Find the marginal product of each input. b) Determine whether the production function exhibits diminishing marginal product to each input. c) Find the marginal rate of technical substitution (MRTSLK) d) How does MRTSLK change as more L, is used holding output constant. e) Find the least costly combination of labour and capital to produce 3000 units.
If the average cost function of a good is 15 AC = +20 + 11 '이 find the fixed costs and an expression for the marginal cost function. The fixed costs are (Type a whole number.) The expression for the marginal cost function is (Simplify your answer. Type an expression using Q as the variable.)
a. A firm's long-run total cost can be written as LTC = 3000Q - 50Q2 + (1/3)Q3 and its long-run marginal cost by LMC = 3000 - 100Q + Q2. Find the range over which the firm will experience economies of scale. Explain your answer. b. A firm has a production function of Q = K * L + L, where the marginal product of labor is MPL = K + 1 and the marginal product of capital is MPK = L. The wage rate (W) is $100 per worker and the rental price (R) is $100 per unit of capital. In the short-run, capital (K) is fixed at 4. Find the minimum total cost of production in the short- and long-run if the firm produces 100 units of output.
Suppose a firm’s cost function is given by: C= 50 + 4q2 a) Find the equations for AFC, AVC and MC. b) If w=$4, what’s the short run production function for this firm?
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.
Provide a diagram that illustrates, for the short-run analysis, the average cost function, the marginal cost function, the average variable cost function and the variable cost function. Provide clear explanations for why these functions have common points of intersection.
Suppose w= 1 and r= 3. Solve the cost minimization problem to find L*(q) and K*(q). Then find the cost function C(q).
Consider the following short run cost function: TC = 4Q³ - 24Q² + 16Q + 100 Derive the expressions for marginal cost and average total cost. What can we infer about the range of output over which production shows increasing returns to labor and diminishing returns to labor?
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.

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