Explore BrainMass

Short- and Long-Run Cost Functions

To understand short and long run cost functions, it is important to understand the concept of cost. A cost is the value of inputs that are used to produce output. Total cost (TC) is the total cost of producing a given level of output and is divided into total fixed cost (TFC) and total variable cost (TVC). Total fixed cost does not change with the level of output and total variable cost does change with the level of output.

A cost function C(q) is a function that shows what the minimum cost for producing q units of output is. Labour is denoted as (L) and Capital as (K). So, with w as the cost of labour per unit and r as the cost per unit of capital, the production cost is:

w * L + r * K

Total cost can be divided into fixed cost, which is independent of quantity, and variable cost, which is dependent on quantity:

C(q) = FC + VC(q)

In the short run, at least one input is fixed and cost curves are defined as operating curves. In the short run, the level of output that correlates to the minimum average total cost is called the capacity of the firm. Since firms cannot change capital:

r * K = constant

When a firm produces less output than the minimum average total cost, it has excess capacity.

In the long run, all inputs are variables (so K and L are variable) and cost curves are defined as planning curves. The long-run average cost curve shows the lowest cost of producing at a certain level of output.

Short and long run cost functions are an integral part of mathematical economics and important to understanding and representing the role of technology in the production process.



Short run and long run cost functions: Profit maximization

1. The demand and cost function for a company are estimated to be as follows: P(Q)=100-8Q; C(Q)=50+80Q-10Q^2+0.6Q^3 (a) What price should the company charge if it wants to maximize profits in the short-tun? (b) What price should ti charge it it wants to maximize it's revenue? (c) Assume the company is a monopoly - what woul

Bank Branch: Performance Measure

I need to write an essay on this and I am completely stuck. The firm has to be a bank branch. Begin by briefly explaining the business, the product(s) and input(s). Clearly explain the measure of output per period and the measure of input per period. Try to provide numerical examples, show how it is used, and (if possible)

Determine the profit-maximizing output and price under 3 scenarios.

Using the function C(Q) = 400+50Q+5Q^2 determine the profit-maximizing output and price and discuss its long-run implications under 3 scenarios. 1) The firm is a perfect substitute with a similar product offered by Firm B, Firm C that have similar cost functions and that currently sell for $200 each. 2) The firm firm has N

Production Function and Marginal Product of Labour

2. Assume the Production Function for Hamburgers is Q = 4L^.50K.^33. where Q is the quantity of hamburgers, L is the number of workers employed and K is number of grills. a. What is the quantity of hamburgers produced when the company employs 64 workers & 36 machines? b. Continue to assume the input mix given above—

Short Run Profit Margin

1. Locate and explain how the optimal output maximizes the per unit profit (II). 2. What happens to profit if outputs are below or above the optimal output level? 3. Summarize the short run profit. Use numbers. Refer to the attached image for more information on the numbers to include in the calculations and how to present

Determining Profit Maximizing Quantity

Your family operates a car wash. There are many other car washes around. You have observed that the customers care only about finding the cheapest price for car washes; they do not care which company they use. To purchased the equipment and the building for the car wash, your have to take out a small business loan. The cost of t

Bundled Pricing for Cable

The reservation prices of three classes of demanders of the cable channels Lifetime, Disney, and ESPN are given below: Class Lifetime Disney ESPN 30 Year Old Males $ 7 $1 $22 30 Year Old Females $20 $10 $15 7 to 12 year olds $ 3 $21 $12 It costs $6 to produce and distribute each channel.

Fixed and Variable Costs Comparison

Production Manager at AutoEdge, Sam Busch, is new to the company. He asks to meet with you to discuss some questions he has. "Thanks for meeting with me on such short notice," he says. "I'm still getting familiar with the situation here, and I could use your help." "Certainly," you say. "And congratulations on your new po

Managerial Economics: Mergers and Market Equilibrium

In 1989, the Detroit Free Press and Detroit Daily News (the only daily newspapers in the city) obtained permission to merge under a special exemption from the antitrust laws. The merged firm continued to publish the two newspapers but was operated as a single entity. a. Before the merger, each of the separate newspapers

Advantages of SEC quarterly reporting

The Theory of the Firm document, the Friedman article, argue that the main goal of a firm in a market economy is to maximize profit (shareholder wealth) over the long term. However, SEC regulations require U.S. corporations to publish operating results on a quarterly basis. How does this short term time frame impact long term pr

Economics: Demand, Supply and Cost Profile

An airline ticket costs the same from Casper, Wyoming to Denver, Colorado, and from Denver to Orlando, Florida. Does this make economic sense and if so what is rationale behind equal prices for unequal distances in air travel using supply, demand, and cost curves?

Production Cost and Profits

1. Suppose a firm is operating at the minimum point of its short-run average total cost curve, so that marginal cost equals average total cost. Under what circumstances would it choose to alter the size of its plant? 2. Explain: In the short-run, why might a firm still operate even when there is a loss? 3. Suppose a firm

What are voluntary export restraint (VER) agreements? Why do some governments force foreign exporters into them instead of just using quotas or tariffs to restrict imports by the same amounts? Is it because VERs bring the importing country a bigger national gain than quotas or tariffs?

What are voluntary export restraint (VER) agreements? Why do some governments force foreign exporters into them instead of just using quotas or tariffs to restrict imports by the same amounts? Is it because VERs bring the importing country a bigger national gain than quotas or tariffs?

Suppose that the current market rate of interest is 10 percent. The market rent on a parcel of land is $6,000 per year. A 10-percent land tax is imposed. As a result of the tax, the price of the land parcel: falls from $60,000 to $30,000. increases from $30,000 to $60,000. falls 10 percent. falls 20 percent. According to the Harberger model of the incidence of the corporate income tax, the tax: reduces the return to capital in the corporate sector of the economy only. reduces the return to capital in all uses. has no effect on the return to capital. increases the return to capital. If corporations maximize profit, a corporate income tax: has no affect on the profit-maximizing output in the short run. reduces the profit, maximizing output in the short run. increase the profit, maximizing output in the short run. increases the supply of corporate output in the short run. Assuming that corporations maximize profits and investors seek to maximize the return to their investments, the long-run impact of a corporate income tax is to: reduce the incomes of corporate shareholders only. reduce the incomes of workers only. reduce the incomes of all investors. increase the price of both corporate and non-corporate goods.

Suppose that the current market rate of interest is 10 percent. The market rent on a parcel of land is $6,000 per year. A 10-percent land tax is imposed. As a result of the tax, the price of the land parcel: falls from $60,000 to $30,000. increases from $30,000 to $60,000. falls 10 percent. falls 20 percent. According


Currently, at a price of $1 each 100 popsicles are solid per day in the perpetually hot town of Rostin. Consider the elasticity of supply. In the short run, a price increase from $1 to $2 is unit-elastic (E5=1.0), So how many popsicles will be sold each day in the short run if the price rises to $2 each? In the long run, a price

Using Non-Price Competition

What is â??non-price competition?â?? Why would any seller use this form of competition? Is the use of this form of competition costless to the user? What is the optimum amount of non-price competition by a firm? What would be the likely response of a sellerâ??s rivals? Who benefits from this competitive device in the shor

Discuss concentration ratios and predict long term adjustments

An industry has 20 firms and a concentration ratio of 30%. If you were in this industry and there was an increased demand for the product that pushed up the price of the goods, what long run adjustments would you expect? And what does your anticipated adjustment process imply about the concentration ratio for the industry?

Long run profits in an increasing-cost industry.

Suppose you own a home remodeling company. You are currently earning short run profits. The home remodeling industry is an increasing-cost industry. In the long run, what do you expect will happen to: A) Your firm's cost of products? Explain. B) The price you can charge for your remodeling services? Why? C) Profits in home

Calculating a Firm's Concentration Ratio

A firm's average cost is $20 and it charges a price of $20. The Lerner index for this firm is: A industry is comprised of ten (10) firms, each with an equal market share. What is the 4-firm Concentration ratio of this industry?

Optimal pricing is assessed.

The US cigarette industry has negotiated with Congress and government agencies to settle liability claims against it. Under the proposed settlement, cigarette companies will make fixed annual payments to the government based on their historic market shares. Suppose a manufacturer estimates its marginal cost at $1.00 per pack, it

Impact of disaster on price of products

Please help with the following problem. Say there is a natural disaster, which wipes out all of the tomato plantation of one country. Therefore, there is a drastic rise in the price say from $6 to $15 a kilo. How has the disaster caused such a drastic price rise in the short-run and how will the outcome be different in the e


1. Assume Amanda Herman finds that her total spending on compact dics remaing the same after the price of compact fall, other things equal. Which of the followin is true about Amanda's demand for compact dics with the price change. (a) It is perfectly price inelastic (b) unit price elastic (c) it is perfectly price elastic (d


Consider the attached aggregate model. Which of the following could cause equilibrium to move from point a to point b? 1. A temporary reduction in aggregate supply 2. An adverse supply shock 3. A beneficial supply shock 4. A gradual decrease in resources

Short Run to Long Run

Carefully explain what will happen as we move from the short run to a long run equilibrium in a monopolistically competitive industry if firms are making a positive profit in the short run. Your explanation should clearly state what will happen to the demand curve facing an individual firm and the reason why this happens.

TC = 10,000 + 100Q + 0.02Q^2 Qd =20,000 - 100 P

The manufacturer of high-quality flatbed scanners is trying to decide what price to set for its product. The cost of production and the demand for the product are assumed to be as follows: TC = 10,000 + 100Q + 0.02Q^2 Qd =20,000 - 100 P a) Algebraically determine the short-run profit maximizing price and quantity. b)

Cost analysis short run and long run

Using the information in the following table: a- Complete the last 2 columns by replacing the * with the correct values. b- Draw the following curves in one chart â?¢ Short-run average product (AP) curve; â?¢ Short-run marginal product (MP) curve. Table showing the Average and Marginal product of labor for a h

Marginal Cost Schedule and Outputs

Suppose that the firm's cost function is given in the following schedule (where Q is the level of output). Output Q (units) Total Cost 0 7 1 25 2 37 3 45 4 50 5 53 6 58 7 66 8 78 9 96 10 124 Determine the: (a) Marginal cost schedule (b) What is the fixed cost of production