Fundamentals Of Managerial Economics Chapter 6 Problems

Fundamentals of Managerial Economics
Problemas capitulo 6
P6.1 Pronóstico de Ventas. Claire Littleton has discovered that the change in product A demand in any given week is inversely proportional to the change in sales of product B in the previous week. That is, if sales of B rose by X percent last week, sales of A can be expected to fall by X percent this week.
A. Write the equation fornext week’s sales of A, using the variables A= sales of product A, B= sales of product B, and t= time. Assume that there will be no shortage of either product.
B. Last week, 100 units of A and 90 units of B ere sold. Two weeks ago, 75 units of B were sold. What would you predict the sales of A to be this week?
Los productos A y B tienen una demanda inversamente proporcional. Cuando la demandade A sube en un porcentaje X, la demanda de B baja en un porcentaje X.
A.
A = ventas del producto A
B = ventas del producto B

B. A = 100 unidades
B = 90 unidades Hace dos semanas = 75 unidades

P6.2 Simultaneous Equations. Supersónic Industries, based in Seattle, Washington, manufactures a wide range of parts for aircraft manufacturers. The company is currently evaluationg themerits of building a new plant to fulfill a new contract with the federal government. The alternatives to expansion are to use additional overtima, to reduce other production, or both. The company will add new capacity only if the economy appears to be expanding. Therefore, forecasting the general pace of economic activity for the United States is an important input to the decision-makinh process.The firm has collected data and estimated the following realtions for the U.S. economy:

Last year´s total profits (all corporations) Pt-1 | =$1,200 billion |
This year´s government expenditures G | =$2,500 billion |
Annual consumption expenditures C | =$ 900 billion + 0,75Y |
Annual investment expenditures I | =$920 billion + 0,9 Pt-1 |
Annual tax receipts T | =0.16 GDP |
Net exportsX | =0.03 GDP |
National Income Y | =GDP-T |
Gross domestic product (IGDP) | =C+I+G-X |
Forecast each of the preceding variables through the simulation relations expressed in the multiple-equation system. Assume that all random disturbances average out to zero.

a. Inversión
I=920+0.9Pt-1
I=920+0.9(1200)
I=2000 billones
b. Product Interno Bruto (PIB)
PIB= =C+I+G-X=900+0.75Y+2000+2500-0.036PIB
=900+0.75 (PIB-0.16PIB) +2000+2500-0.036PIB
=5400+0.66PIB
PIB= =13,500 billones
c. Consumo
C =$900+0.75Y
=$900+0.75(PIB-T)
=$900+0.75(0.846PIB)
=$900+0.63(13500)
=$9405
d. Impuestos
T=0.16Y
T=0.16(13500)
T=2160
e. Y=PIB-T
=PIB-0.16PIB
Y=0.84*13500
Y=11340 billones.

P6.3 Pronóstico de Costos. Dorothy Gale, a quality-control supervisor forWizard Products, Inc., is concerned about unit labor cost increases for the assembly of electrical snap-action switches. Costs have increased from $80 to $100 per unit over the previous three years. Gale thinks that importing switches from foreign suppliers at a cost of $115.90 per unit may soon be desirable.

A. Calculate the company’s unit labor cost growth rate using the constant rate ofchange model with continuous compounding.

B. Forecast when unit labor costs will equal the current cost of importing.

Labor costs han subido de $80 a $100 por unidad en los 3 últimos años. Importar switches cuesta $115.90 por unidad.

A. Modelo de crecimiento constante compuesta continuamente
Log 100 = log 80 + log (1+g)*3
2 = 1.90 + log (1+g)* 3
0.0969 = log (1+g)* 3
0.0323 = log(1+g)
1+g = 1.0772
g = 0.0772 = 7.72%

B. Calcular cuando los costos van a igualar a los costos de importación.
115.9 = 100*(1+0.0772)^t
1.159 = 1.0772^t
ln 1.159 = t ln 1.0772
t = 2 años
P6.4 Cost Forecasting. Mid.Atlantic Cinema, Inc, runs a chain of movie theaters in the east-central states and has enjoyed great success with a Tuesday Night at the Movies promotion. By offering...