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ECON 1100 Chapter Notes - Chapter 7: Production Function, Fixed Cost, Opportunity Cost

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coffeebuffalo475
23 Apr 2016
School
University of Windsor
Department
Economics
Course
ECON 1100
Professor
bajic

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Document Summary

All firms are assumed to be profit-maximizers, seeking to make as much profit for their owners as possible. Each firm is assumed to be a single, consistent decision-making. Max profit = max = revenue total cost (of production) Max = p x q total cost. Firm must decide how much to produce and how to produce it! Production function between q and two inputs (labour and capital) Production function: is the relationship between maximum output attainable and inputs used (l and k) as all inputs vary; changes in f reflect changes in technology. P = equilibrium price of the good (pe) Let"s now assume that q is fixed! (q bar) The company previously decided to fix the amount of output! Max = pe x q(bar) total cost (but pe is also kinda fixed) Max = rev total cost (will be optimised when total cost is minimized) Economic profits = revenues (explicit costs + implicit costs)

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Related Questions

A firm has a production function Q=F(K, L) with the constant return to scale, where k is units of capital and L is united of labour. Input prices are r=$2 per unit of K and w=$1 per unit of L. When it produces 5 units of output, it uses 2 units of capital and 3 units of labour. When its long-run total cost is equal to $70, how much capital and labour it will employ to product how many units of output? What is the long-run average cost?

Suppose that a fully automated production process can produce output according to the production function Q = 10K – 0.5K2 where Q = output and K = capital input. Assume further that the expression for the marginal product of capital, MPK, is given as MPK = 10 – K. In this production process capital costs $90 to rent (MFC = $90) and the output sells for $30 per unit (and therefore P = MR = $30).

a. Based on this information, what is the expression for the marginal revenue product of capital, MRPK in this production process? 

b. Given that the production function has a single variable input, what is the optimal quantity of capital the firm should rent (K*) given the existing rental cost of capital and price per unit of output?

c. Based on the optimal rental of capital, how much output (Q) would this company produce per production period? Total Output (Q) = ____________________.

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 1⁄2 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.