A firm operating in a perfectly competitive market has the following total cost function: TC=0.4Q²+40. Its marginal cost function is given by: MC=0.8Q. There are 20 identical firms in the short-run in the market. In addition, the demand function is given by: Q=300-5P

a) Find the Supply Function for the Firm in the short-run

b) What is the equilibrium price and quantity in the market in the short-run?

c) How much does each of the 20 firms produce in the short-run?

d) How much profits does each firm make in the short-run? Will there be entry or exit in the long-run?

e) If ATC is minimized at Q=10, what is the price of the product in thelong-run?

f) How many firms are in the market in the long-run?

Data for Oriole Corporation’s maintenance costs is shown below.

Compute the variable- and fixed-cost elements using the regression analysis. Present your solution in the form of a cost equation. (We recommend that you use the Intercept and Slope functions in Excel.) (Round intercept to 2 decimal places e.g. 1.25 and slope to 5 decimal places e.g. 1.25125.)

Equity Multiplier

Accounts Receivable Days

ROE (in decimal form, not %)

EPS

P/E

Fixed Asset Turnover:

Operating Margin (in decimal form, not %)

Inventory Turnover

Interest Coverage Ratio (TIE)

Quick Ratio

A company would like to estimate its total cost equation using customer records. The company has randomly sampled 28 customer records. Each customer record contains a Customer #, the Order Size, and the Total Cost of the Order. The analyst remembers from accounting and economics classes taken in college that

TOTAL COST = Fixed Costs + Variable Cost per Unit *Order Size.

The analysis sees that this is a linear relationship where the TOTAL COST depends on the Fixed Costs, which do not depend on order size, and a variable cost per unit, which is multiplied by the Order Size. The analysis decides to use simple linear regression to estimate the firm’s Total Cost function. Use the data file, Estimating a Total Cost Regression Model.xlsx to answer the following questions:

1. What is the dependent variable in this analysis? What is the independent variable in this analysis?
2. Use excel to estimate the regression model. State the estimated total cost function.
3. What is the estimated Fixed Cost for the Company? Remember the fixed costs is independent of output. You can estimate it as the Total Cost when output is “0”. (Look at the regression output produced by Excel for part b.)
4. What is the estimated average unit variable cost for the Company? (Look at the regression output produced by Excel for part b.)
5. Develop a 95% confidence interval for the true average unit variable cost. (Look at the regression output produced by Excel for part b.)
6. What percent of the variation in monthly total costs is “explained” by the regression model with monthly production output as the explanatory variable? (Look at the regression output produced by Excel for part b.)
7. Suppose the plant manager is interested in estimating the mean total costs for several months where output is 30,000 units (i.e., Xp = 30) each month. Develop a 95% confidence interval for the mean total costs for months that average 30,000 units of output.

Assume that a competitive firm has the total cost function: TC=1q3−40q2+720q+2000

Suppose the price of the firm's output (sold in integer units) is $700 per unit.

Using tables (but not calculus) to find a solution, what is the total profit at the optimal output level? Please specify your answer as an integer.

1. Refer to the Campus Crime dataset in the EXCEL file. This data comes from a study of 20 campuses selected at random from a list of four-year schools in the continental U.S. Variables include:

• Number of Crimes reported during the most recent reporting year.
• Number of Police on the school’s police force during the most recent reporting year.
• Total Enrollment at the school during the most recent reporting year.
• Total Expenditure ($) on police protection by the school during the most recent reporting year.
• An indicator of whether the school is public or private (1 = Private, 0 = Public)

Further information that may be relevant is that there are 629 public and 1845 private four year institutions in the continental US, enrolling 6.838 million and 4.162 million, respectively during the most recent reporting year.

1. (For part A, assume that you only have columns A and E in the dataset). In an appropriate way, report an interval estimate of the total number of crimes on 4-year college campuses across the U.S. during the most recent reporting year. Briefly also discuss why your method is appropriate.
2. (For part B, you should use any part of the data you determine to be relevant). In an appropriate way, report an interval estimate of the total number of crimes on 4-year college campuses across the U.S. during the most recent reporting year. Briefly also discuss why your method is more appropriate than the method you used in (a).
3. Compare and contrast your estimates from (a) and (b). Identify the differences and explain why the estimates are different.
4. (For part D, again use any part of the data you deem relevant). Estimate the protection cost per police officer for all 4-year colleges across the nation. Briefly also discuss why your method is appropriate.
5. (For part E, again use any part of the data you deem relevant). Estimate the protection cost per enrolled student for all 4-year colleges across the nation. Briefly also discuss why your method is appropriate.

10. Suppose a perfectly competitive firm’s demand curve is below its average total cost curve. Under which conditions will a firm continue to produce in the short run?

If the supply curve intersects the marginal cost curve above the average variable cost curve

If the demand curve intersects the marginal cost curve above the average variable cost curve.

11. Study Questions and Problems #11 Suppose the industry equilibrium price of residential housing construction is $100 per square foot, and the minimum average variable cost for a residential construction contractor is $110 per square foot. You should advise the owner of the firm to...….

a. Shut down

b. Decrease output

c. Increase output

12.

Suppose independent truckers operate in a perfectly competitive industry and an increase in demand creates positive economic profits for firms in the short run.

Indicate what happens in the long run to each factor in the following table. (Check all that apply.)

True or False: Given these conditions, the independent trucking industry is a constant-cost industry.

True

False

A U-shaped long-run average total cost curve can be explained by firms increasing their factory size to
(x) avoid coordination problems that occur when the factory is large.
(y) take advantage of greater specialization.
(z) avoid fixed costs.
A. (x), (y) and (z)
B. (x) and (y) only
C. (x) and (z) only
D. (y) and (z) only
E. (y) only

A business firm produces and sells specialty cakes. Last year, the firm produced 12,000 cakes and sold each cake for $20. In producing the 12,000 cakes, it incurred variable costs of $150,000 and a total cost of $183,000. Which of the following statements is (are) correct?
(x) The firm’s economic profit for the year was more than $51,250 but less than $54,375.
(y) Fixed costs amounted to $33,000 and average fixed costs are $2.75 per unit for 12,000 cakes.
(z) In producing the 12,000 specialty cakes, the firm’s average variable cost was more than $12.25 per cake and its average total cost was less than $15.75 per cake.
A. (x), (y) and (z) B. (x) and (y) only
C. (x) and (z) only D. (y) and (z) only E. (y) only

Which of the following statements is (are) correct?
(x) If marginal cost is $10 and rising, average variable cost could be either greater than or less than $10.
(y) If you know the average variable cost of 75 units then you have sufficient information to calculate the marginal cost of the 75th unit.
(z) If you know the average fixed cost of 600 units then you have sufficient information to calculate the average fixed cost of 400 units.
A. (x), (y) and (z) B. (x) and (y) only
C. (x) and (z) only D. (y) and (z) only
E. (x) only

1. The sunflower oil industry is perfectly competitive. Every producer has a following long-run total cost function given by TC(Q) = 2Q³− 15Q² + 40Q where Q is measured in tons of sunflower oil.
   1. What is the marginal cost for an individual firm?
   2. Calculate and graph the long-run average total cost of producing oil that each firms faces for values of Q from 1 to 10.
   3. What will the long run equilibrium price of sunflower oil be?
   4. How many units of sunflower oil will each firm produce in the long run?
   5. Suppose that the market demand for canola oil is given by Q = 999 − .25P. At the long-run equilibrium price, how many tons of sunflower oil will consumers demand?
   6. Given your answer to part e, how many firms will exist when the industry is in the long-run equilibrium?

Suppose a competitive firm has as its total cost function: TC=26+3q2 T C = 26 + 3 q 2 Suppose the firm's output can be sold (in integer units) at $61 per unit. Using calculus and formulas (don't just build a table in a spreadsheet as in the previous lesson), how many integer units should the firm produce to maximize profit? Please specify your answer as an integer. In the case of equal profit from rounding up and down for a non-integer initial solution quantity, proceed with the higher quantity.