A. A competitive firm has a short run total cost curve represented by the following equation:C(q) = q2/4 + 50

a. (4) Derive how many units a profit maximizing competitive firm produce as a function of P(price)(qs(p)=).

b. (2) If there are 100 firms in the market, derive the supply curve.

c. (6) The market demand is 1200 –100P derive the market price and the firm’s profit.

d.(2)Given your answer in c, explain what will start to happen in the long run.

B. Graph a competitive firm that would operate in the short run, but exit in the long run. Show its optimal output, revenue and COSTSsuch that it would operate in the short run but not the long run. Include all curves needed for this..

Monopolistic firm has the inverse demand function p = 250 – 5Q. Firm’s total cost of production is C = 1250 + 10Q + 8Q² :

1. Create a spreadsheet for Q = 1 to Q = 20 in increments of 1. Determine the profit-maximizing output and price for the firm and the consequent level of profit.

2. Will you continue the production at the profit-maximizing level of output? Show why or why not?

3. Calculate the Lerner Index of monopoly power for each output level and verify its relationship with the value of the price elasticity of demand at the profit-maximizing level of output.

4. Now suppose that a specific tax of 10 per unit is imposed on the monopoly. What is the effect on the monopoly’s profit-maximizing price?

Quality Cost Report

Evans Company had total sales of $3,000,000 for fiscal 2015. The costs of quality-related activities are given below.

Required:

1. Quality Cost Report

   Evans Company had total sales of $4,800,000 for fiscal 20x5. The costs of quality-related activities are given below.

   Returns/allowances	$240,000
   Design changes	360,000
   Prototype inspection	14,400
   Downtime	312,000
   Quality circles	9,600
   Packaging inspection	14,400
   Field testing	14,400
   Complaint adjustment	264,000

   Required:

   1. Prepare a quality cost report, classifying costs by category and expressing each category as a percentage of sales. Round percentages to one decimal place, when rounding is required. For example, 5.78% would be entered as "5.8".

   Evans Company
   Quality Cost Report
   For the Year Ended 20x5
   	Quality Costs	Total	Percentage of Sales
   Prevention costs:
   	$
   		$	%
   Appraisal costs:
   	$
   Internal failure costs:
   	$
   External failure costs:
   	$
   Total quality costs		$	%

If the total cost function for a product is C(x) = 8(x + 5)^3 dollars, where x represents the number of hundreds of units produced, producing how many units will minimize average cost? x = hundred units

Find the minimum average cost per hundred units. $

Estimation of production cost, total capital investment and profitability analysis for Benzalkonium chloride

Benzalkonium is especially known for its antimicrobial activity, benzalkonium chloride is an active ingredient in many consumer products:

 Pharmaceutical products such as eye, ear and nasal drops or sprays, as a preservative

 Personal care products such as hand sanitizers, wet wipes, shampoos, soaps, deodorants and cosmetics

 Skin antiseptics and wound wash sprays, such as Bactine.

 Throat lozenges and mouthwashes, as a biocide

It is desired to produce 100 000 tons of Benzalkonium chloride annually. We have a patent for “METHOD FOR PRODUCING ALKYLDIMETHYLBENZYLAMMONIUM CHLORIDES” and we wish to produce our chemical-based on this patent.

Determine the fixed capital investment, working capital investment, production cost, net profit after taxes and draw a cumulative cash position graph.

In your project use the patent given to you. You may need to make assumptions if you can not find data from the literature. You should give your claims for each assumption you make.

Good Luck.

Patent No: EP 1 505 058 A1 “METHOD FOR PRODUCING ALKYLDIMETHYLBENZYLAMMONIUM CHLORIDES”

A competitive industry includes a large number of identical firms. Each firm has the total cost function TC(q) = q2 + 25. It can be shown that each firm’s marginal cost function is MC(q) = 2q.

a. Derive an equation for a single firm’s supply equation..

b. Derive the individual firm’s average total cost equation. Show your work. Now suppose the market price of the firms’ output is $8.

c. What will each firm’s profit-maximizing output be equal to?

d. What is each firm’s profit equal to at its profit-maximizing output?

consider long run equilibrium

What (if anything) will happen to the number of firms in this industry in the long run? Will it rise, fall, or stay the same? Why? Carefully explain.

f. What will be the equilibrium market price in this market in the long run? Why? Show your work and carefully explain.

A company operates two plants which manufacture the same item and whose total cost functions are C1=6.4+0.04(q1)^2 and C2=7.9+0.02(q2)^2 where q1 and q2 are the quantities produced by each plant. The company is a monopoly. The total quantity demanded, q=q1+q2, is related to the price, p, by p=40−0.02q How much should each plant produce in order to maximize the company's profit? q1=? q2=?

1.a. A competitive firm has a short run total cost curve represented by the following equation:

C(q) = 50 + .05q2

Derive the marginal cost. Derive the expressions for average total cost and average variable cost for this C(q)

b. In the short run, if the price is $4, what is marginal revenue? How many units should a profit maximizing competitive firm produce? What is its profit (loss)? Would this firm produce in the short run (long run) at this price? If the price is $20, how many units does a firm produce? What is its profit or loss?

c. What is the firm's short run supply curve (an equation: qs=)? Hint: how did you know how many units the firm produces at each price?

d. If there are 50 identical firms in this market, what is the supply curve? If the market demand Qd= 5000-500P, what is the amount sold and the market price? What do profits for the individual firm equal?

e. What happens in the long run?

Please answer all parts