DEPARTMENT OF ECONOMICS
Economics 340H – WI 07
Assignment #1
Instructor: Christopher Michael
Due Date: Oct 11, 2007
Question 1 – Risk Analysis
A firm has decided to invest in a piece of land. Management has estimated that the land can be
sold in 5 years for the following possible prices:
Price
10,000
15,000
20,000
25,000
Probability
0.20
0.30
0.40
0.10
a) Determine the expected selling price for the land.
b) Determine the standard deviation of the possible sales prices.
c) Determine the coefficient of variation.
Question 2 – Risk Analysis
Southern New Hampshire University’s marketing department has to decide which of the two
advertising strategies to adopt: Strategy A – Advertise on spot billboards and transportation
vehicles (bus / subway) or Strategy B – Advertise in national newspapers / magazines. The
recruitment office has estimated student enrolment assumptions and their probabilities under each
alternative plan as given in the following pay-off table:
Strategy A
Enrolment
8,000
12,000
16,000
Probability
0.25
0.50
0.25
Strategy B
Enrolment
8,000
10,000
16,000
Probability
0.30
0.40
0.30
a) Calculate the expected enrolment under each strategy.
b) Chart the probability distribution of the expected enrolment under each strategy.
c) Calculate the standard deviation of the distribution of enrolment for each marketing
strategy.
d) Which of the two strategies is more risky for SNU and why?
e) Which strategy should SNU choose and why (Hint – Use coefficient of variation)?
Question 3 – Demand Theory
The manager of the Sell-Rite store accidentally mismarked a shipment of 10-kilo bags of charcoal
at $4.38 instead of the regular price of $5.18. At the end of a week, the store's inventory of 200
bags of charcoal was completely sold out. The store normally sells an average of 150 bags per
week.
(a) What is the store's arc elasticity of demand for charcoal?
(b) Give an economic interpretation of the numerical value obtained in part (a)
Question 4 – Economic Optimization
Presto Products, Inc., manufactures small electrical appliances and has recently introduced an
innovative new dessert maker for frozen yogurt and fruit smoothies that has the clear potential to
offset the weak pricing and sluggish volume growth experienced during recent periods.
Monthly demand and cost relations for Presto's frozen dessert maker are as follows:
P = $60 - $0.005Q
A.
TC = $100,000 + $5Q + $0.0005Q2
MR = TR/Q = $60 - $0.01Q
MC = TC/Q = $5 + $0.001Q
Set up a table or spreadsheet for Presto output (Q), price (P), total revenue
(TR), marginal revenue (MR), total cost (TC), marginal cost (MC), total profit
(π), and marginal profit (Mπ). Establish a range for Q from 0 to 10,000 in
increments of 1,000 (i.e., 0, 1,000, 2,000, ..., 10,000).
B.
Using the Presto table or spreadsheet, create a graph with TR, TC, and π as
dependent variables, and units of output (Q) as the independent variable. At
what price/output combination is total profit maximized? Why? At what
price/output combination is total revenue maximized? Why?
C.
Determine these profit-maximizing and revenue-maximizing price/output
combinations analytically. In other words, use Presto's profit and revenue
equations to confirm your answers to part B.
D.
Compare the profit-maximizing and revenue-maximizing price/output
combinations, and discuss any differences. When will short-run revenue
maximization lead to long-run profit maximization?
Question 5 – Demand Theory
Hanna Corporation markets a compact microwave oven. In 2005 they sold 23,000 units at $375
each. Per capita disposable income in 2005 was $6,750. Hanna economists have determined that
(a) In 2006 Hanna is planning to lower the price of the microwave oven to $325. Forecast sales
volume for 2006, assuming that all other things remain equal.
(b) However, in checking with government economists, Hanna finds that per capita disposable
income is expected to rise to $7,000 in 2006. In the past the company has observed an arc
income elasticity of +2.5 for microwave ovens. Forecast 2006 sales given that the price is
reduced to $325 AND that per capita disposable income INCREASES to $7,000. Assume that
the price and income effects are independent and additive.