Need these solved

Case Study # 4: Perfect Competition (35 pts total)

Please write answers in this Word document in red.Please be sure any graphs are imbedded in the document for the appropriate question.

You will need results/graphs from Case Study #3 to complete this study.

General Case Information:

This case study focuses on a perfectly competitive industry

Each competitive firm in this industry has a Cobb-Douglas production function:

These firms combine capital and labor to produce output

The price of capital and labor are:r = .05 and w = 45

In this case study, you will: use graphs and equations to analyze competitive firm decisions, the interaction between those decisions and the competitive market determination of price.

Skills needed to complete this case study:

1. Enter data, enter formulas, and create charts in Excel
2. Use basic algebra

Perfect Competition (35 pts)

1.(9pts) Find equilibrium P & Q in the perfectly competitive market.Demand is represented by the equation:Q = 1500 - 2P.The perfectly competitive firms are assumed to be identical.The quantity supplied by each individual firm is represented by the firm's MC curve.In order to graph market supply and market demand, however, we need to focus on market quantity, rather than individual firm quantity.The market quantity is equal to; where q is the individual firm's quantity and n is the number of firms in the industry.

a.(2pt) What is the equation for the individual firm's SR supply curve?Recall your graphs from Case Study 3, question 4. Notice that MC and AVC are both linear.Recall that MC = 25q.Use both profit maximizing rules to find your individual SR supply function (get q as a function of P).

b.(1pt) Suppose there are 100 firms in this industry.What is the equation of the SR market supply curve?

c.(2pts) Solve for the short-run market equilibrium (find equilibrium P & Q using algebra).

d.(2pts) Calculate the inverse demand curve.Calculate the inverse supply curve.Show your work.You will need these inverse functions in order to graph S and D.

e.In Excel, copy your "cost" worksheet from Case Study #3 into sheet4 (it may be labeled sheet 3).Do this by right clicking on "cost" and choosing "move or copy."A box will appear.Click the box at the bottom that says, "create a copy."In the box above, click on "sheet4" (or "sheet3") then click ok.This will create a copy of your cost worksheet.It will be named "cost(2)" - rename it "perfect comp"

f.(2pts) Graph Supply and Demand curves.Generate new columns in Excel to represent demand and supply.This will require some strategic thinking.You will want to generate a graph with market quantity on the horizontal axis.That means that you will need to generate a column of numbers to represent possible values of market quantity.

Let column K represent market quantity, .

Store values for market demand prices in column L.Use the inverse demand curve from 6d.

Store values of market supply in column M using inverse supply equation.Notice that the numbers in column M are equal to the numbers representing MC in column I.

Create S and D graph.Title the graph "Market S & D" and label the axes.Format the graph so the max on the horizontal axis is 2000 and the min on the vertical axis is 0.Make sure there are major grid lines going both directions.Verify that the computed equilibrium P & Q are consistent with the graph.Copy and paste your graph here:

2.(9pts) Calculate profit for a single perfectly competitive firm in this market.

a.(2pts) Given the equilibrium market price found in question 6, use the profit-maximizing rules to determine the optimal level of output for the individual firm to produce (q^*).Show work.

b.(1pt) Calculate the total revenue that this firm earns from selling q^*.

c.(2pts) Calculate the total cost that this firm incurs in the short run by producing q^*.Recall your SR cost functions found in Case Study #3.How much of this cost is fixed cost and how much is variable cost?

d.(1pt) Calculate this firm's profit from producing and selling q^*.

e.(1pt) Fill out the table below with your answers:

Total Revenue

Total Cost

FC

VC

Profit

f.(2pts) What will happen in the long run?Explain.

3.(5pts) Generate a graph to show the optimal quantity that will be produced by each competitive firm, and the resulting profit.This graph will include 4 curves:

The short-run equilibrium price (To generate this horizontal line, use column J to store the values of the equilibrium P.Because this line is horizontal, all of the numbers stored in this column are identical.)

ATC

AVC

MC.

a.(3pts) Use scatter-plot to generate this graph using columns E-J (you can delete data from AFC column if you wish).Title the graph "PC in SR - firm level" and label the axes.Format the graph so the max on the horizontal axis is 20, the max on the vertical axis is 500, and there are major grid lines both ways.Drag the bottom down a bit to make the graph easier to see.Create dots on the MC and the ATC curves at the profit-maximizing level of q (Click on each point twice, right click and click "format data point." Click "marker options" and choose "built-in."From the drop-down menu, choose the circle and increase its size to 7.Click close).Cut and paste your graph here:

b.(1pt) On the graph above, shade in the area of profit (do this by hand).

c.(1pt) Is your graph consistent with your profit computation?Explain.

4.(12pts) You work for a firm that produces an input that is used by these competitive firms.Your marketing vice president has asked you to provide an analysis to support the marketing department's strategic planning committee.They understand that the industry is not currently in long-run equilibrium, and they have asked you to help them estimate the output that will be produced and the number of firms that will exist when the industry reaches long-run equilibrium.They assume that all firms have the same production function and cost structure.This will require several steps:

a.(2pts) For each firm, the LR equilibrium occurs when profit equals zero.This means that P=ATC.The quantity rule requires that P=MC, thus, at the LR equilibrium, P=MC=ATC.Using this information, calculate q^* and P that satisfy both conditions.

b.(1pt) In the market, S & D must be equal at this price.In other words, this must be a market equilibrium price.Calculate the equilibrium market quantity (Q^*).

c.(1pt) Use the market Q and the individual firm q to find the number of firms now operating in the market.

d.(2pts) What is the equation of the new market supply curve?Find the inverse market supply curve.This is the LR equilibrium market supply.

e.Draw the pair of graphs that depict long run competitive equilibrium.To create graphs, complete the following steps:

Return to your "perfect comp" worksheet

Replace the price in column J with the new price you calculated above.

(2pts) Use scatter-plot to create a graph that shows the LR equilibrium for the firm.Only include ATC, MC and your new P.Title the graph "PC in LR - Firm Level" and label the axes.Format the graph so the max on the horizontal axis is 20, the max on the vertical axis is 500, and there are major grid lines both ways and minor vertical grid lines.Drag the bottom down a bit to make the graph easier to see.Cut and paste your graph here:

Verify that the long run equilibrium is consistent with what you calculated.

In column N, enter the formula for the new inverse market Supply.

(2pts) Use scatter-plot to create a graph that shows market Demand and both the initial market Supply and the long-run equilibrium market Supply.Title the graph "Final Market S & D" and label the axes.Format the graph so the min on the vertical axis is 0, the max on the horizontal axis is 2000 and there are major grid lines both ways and minor vertical grid lines. Copy and paste your graph here:

Verify that the short-run and long-run equilibrium prices and quantities are consistent with your algebraic solution values.

(2pts) Complete the following summary table:

Short Run Equilibrium

Long Run Equilibrium

Output of each individual firm

Industry output

Number of firms

Profit for each firm