For TFP to be the primary cause of business cycles, what must hold with respect to substitution and income effects for leisure? Explain in the context of 1-period, closed economy model.

Differential Geometry

Open & Closed Sets, Continuity

Prove f(t)=(x(t),y(t)) is continuous iff x(t) and y(t) are continuous

The highest and lowest birth rates in the United States in 2010 were in Utah and Maine, respectively. Utah reported 52,258 births with a population of about 2.8 million people. Maine reported 12,970 births with a population of about 1.3 million people. Use this data to answer the following questions.

a) On average, how many people were born each day of the year in Utah?

b) On average, how many people were born each day of the year in Maine?

c) What was the birth rate in Utah in births per 100,000 residents?

d) What was the birth rate in Maine in births per 100,000 residents?

The condensed income statement for the Terri and Jerri partnership for 2010 is as follows.
TERRI AND JERRI COMPANY
Income Statement
For the Year Ended December 31, 2010
Sales (200,000 units)
Cost of goods sold
Gross Profit
Operating expenses
Selling
Administrative
Net Loss
$280,000
160,000
$1,200,000
800,000
400,000
440,000
($40,000)
A cost behavior analysis indicates that 75% of the cost of goods sold are variable, 50% of the selling expenses are variable, and 25% of the administrative expenses are variable.
Instructions: (Round to nearest unit, dollar, and percentage, where necessary.)
(a) Compute the break-even point in total sales dollars and in units for 2010.
(b) Terri has proposed a plan to get the partnership “out of the red” and improve its profitability. She feels that the quality of the product could be substantially improved by spending $0.25 more per unit on better raw materials. The selling price per unit could be increased to only $6.25 because of competitive pressures. Terri estimates that sales volume will increase by 30%. What effect would Terri’s plan have on the profits and the break-even point in dollars of the partnership? (Round the contribution margin ratio to two decimal places.)
(c) Jerri was a marketing major in college. She believes that sales volume can be increased only by intensive advertising and promotional campaigns. She therefore proposed the following plan as an alternative to Terri’s. (1) Increase variable selling expenses to $0.79 per unit, (2) lower the selling price per unit by $0.30, and (3) increase fixed selling expenses by $35,000. Jerri quoted an old marketing research report that said that sales volume would increase by 60% if these changes were made. What effect would Jerri’s plan have on the profits and the break-even point in dollars of the partnership?
(d) Which plan should be accepted? Explain your answer

When Apple introduced the iPod in 2001, the iPhone in 2007 and the iPad in 2010, it substantially innovated respectively the multimedia player, the smartphone and the tablet industry. Consider the demand for an innovative Apple product y as D(p) = 1000 – p, and a cost function of c(y)=200∙y.

1. At first consider Apple having a monopoly in this market. What is the inverse demand curve p(y)? With profits being π = p(y)∙y – c(y), what is the profit maximizing quantity y? What is the corresponding price p? What is profits π and what is the consumer surplus CS?

2. Soon after another firms enters with a virtually identical product, and a leader-follower dynamic ensues. Overall industry output is Y = y₁ + y₂, where y₁ is the leader Apple product and y₂ is the follower competitor product. The inverse demand curve you derived in part a is now p(Y) and Apple’s profits are π₁ = p(Y)∙y₁ – c₁(y₁) and the competitor’s profits are π₂ = p(Y)∙y₂ – c₂(y₂), where c₂(y₂) = 200y₂. Find the competitor’s reaction function y₂=R₂(y₁).

3. Being the industry leader, Apple is well aware of how the follower will react once Apple decides its production capacity. What is Apple’s optimal production level y₁? Substitute R₂(y₁) into Y and maximize π₁ with respect to y₁. How does this y₁ compare to the output level you found in part a? How does the leader quantity decision making differ from a monopolist?

4. Given y₁ you determined in part c, what is y₂? Plug y₁ into R₂(y₁). Given y₁ and y₂, what is Y? What is the market price p and how does it compare to what you found in part a? What are profits π₁ and π₂? What is the consumer surplus now, and how does it compare to the one you found in part a?

THe Golfing Statistics provides data for a portion of the 2010 professional season for the top 25 golfers.

A) Find the best multiple regression model for predicting earnings/event as a function of the remaining variables.

B) Find the best multiple regression model for predicting average score as a function of the other variables except earning sand events.

On January 1, 2010, the Felix Company purchased a machine to use in the manufacture of its product. The invoice cost of the machine was $260,000. At the time of acquisition, the machine had an original estimated useful life of 10 years and an estimated salvage value of $20,000. Annual depreciation was recorded at $24,000 per year. The machine was depreciated using the straight-line method. On August 1, 2015, Felix exchanged the old machine for a newer model. The new machine had a fair market value of $200,000. The estimated fair value of the old machine was $150,000. Felix also paid $50,000 as part of the exchange transaction. The old machine was depreciated on Felix’s books up through December 31, 2014.

1. Bring Felix’s depreciation on this machine up to date through the date of the exchange.