ECON20002 Lecture Notes - Lecture 14: Marginal Cost, Marginal Product, Production Function

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orchidgnu53

27 Jul 2018

School

University of Melbourne

Department

Economics

Course

ECON20002

Professor

Reshad Ahsan

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Document Summary

If k is fixed and l is variable then: fc = rk and vc(q) = wl*(q) Firms can vary both labour and capital to minimise costs. Can be fixed costs won"t be due to fixed factors of production. To minimise costs of producing q1 the firm must find the lowest isocost line that is tangent to the isoquant q1. Since the slope of the isocost is -w/r, hence at the optimum point the following relationship holds: Optimal point slope of isoquant = slope of isocost. Lhs is additional output from spending more on labour. Rhs is additional output from spending more on capital. Deriving the cost-minimising input choice to produce output involves using the following conditions: Optimal input choice must satisfy the tangency condition. Optimal input choice must be on the production function. Two equations yield the optimal input choices (l*, k*) as functions of w, r, and q0. Known as conditional input demands for the firm.

Related Questions

3. A firm has a long-run production function:

(a) In the short run, K = 81 is fixed. Find the short-run production function. What is the marginal product of labor in the short-run?

(b) If w = 10 and r = 15.24, find the short-run cost function. To do this, first, figure out how many workers are needed to produce Q units of output, and then add up the (fixed) SR cost of capital and the cost of labor as a function of Q. How many workers are needed to produce Q = 10?

(c) Write down equations for an average total cost (ATC) and average variable cost (AVC) as a function of Q. What is ATC when Q = 10? What as AVC when Q = 10?

(d) Write down the equation for the marginal cost (MC) as a function of Q. What is the marginal cost of producing Q = 10 in the short run?

(e) Verify that MC = w*MPL, evaluating the marginal product of labor from part (3a) at the number of workers needed to produce 10 units of output.

(f) In the long run, both capital and labor are variable. Find the marginal product of labor and the marginal product of capital. Find the marginal rate of technical substitution. On a properly-labeled graph, draw an isoquant for Q = 10.

(g) Does the production function exhibit increasing, decreasing, or constant returns to scale?

(h) Find the lowest cost method of producing Q = 10 (two unknowns: K and L). To do this, equate the MRTS with the input price ratio w r (one equation) and use the isoquant for Q = 10 as the second equation.

(i) Use the fact that the cost, in the long run, is wL + rK to find the LR cost of producing Q = 10. What is the long-run average cost (LRAC) at Q = 10?

(j) (Hard) More generally, use the MRTS and the production function to find the cost of producing any quantity Q. To do this, repeat the above exercise but keep Q as an (unknown) variable, and solve for K and L as functions of Q.

(k) On a properly labeled graph, depict ATC from part (3b) and LRAC from part (3j). Why is LRAC everywhere below ATC?

(l) What is the production level at which SRAC is minimized?

salmonhyena380

Given the following production function, where K (capital) and L (labor), that cost the firm r (rental rate) and w (wage).

Q = 3L^2/3K^2/3

Write down the expression for the production function where fixed capital level is 125 units and only input level that firm can vary is labor.

Based on 1, find MPL and APL.

Find FC, VC(q), AC(q) and MC(q) using information from part 1 and 2. Do these curves describe the firm in the short run or long run?

If a $100 fee is imposed on the company, regardless of production. What are the new values of FC, VC(q), AC(q), and MC(q)?

Imagine that the same firm is free to select any quantity of capital and labor it wants, what types of returns to scale will it experience?

redlion644

Q1) Soundscape Enterprises manufactures Sonoblast, a device that produces a high-pitched reminder to telemarketers that they have once again disturbed you just when you were sitting 1â2 down to dinner. The production function for Sonoblasts is given by the formula Q = 2KL where Q is in units of output per period, K is in machine-weeks per period, and L is in labour- weeks per period. The machine rental rate r is $512 per machine-week and the wage rate w is $128 per labour-week. In the short run, K is fixed at 4 machine-weeks per period.

a. Give the formulas for the short-run production function and the marginal product of labour (MPL) function.

b. Express variable cost (VC), total cost (TC), and marginal cost (MC) as functions of L and as functions of Q; and average variable cost (AVC), average fixed cost (AFC) and average total cost (ATC) as functions of Q.

c. At what level of Q is ATC minimized? What are the values of ATC and of MC at this level of output?

d. If K is increased to a fixed 16 units, at what level of Q is ATC minimized, and what are the values of ATC and of MC at this level of output?

e. In the long run, with all inputs variable, what is the optimal K/L ration with input prices unchanged? How many units of L and of K would be required to produce the levels of output in 1c and in 1d and what is the average cost of producing Sonoblasts in each case? Explain the relation between your results here and those for 1c and 1d.

lilacchinchilla474

ECON20002 Lecture Notes - Lecture 14: Marginal Cost, Marginal Product, Production Function

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