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Elasticities in a Competitive Marketplace

I must know the formulas that are used and I must have the calculations.
Problem 2

A firm has kept track of the quantity demanded of its output (good X) during four time periods. The price of Z and the prices of two other goods (good Y and good Z) were also recorded for each time period. The information if provided in the table below. Use it to calculate the own-price arc elasticity of demand and the two cross-price elasticities of demand. Determine whether good Y and good Z are complements of substitutes for good X.

(see attached file for data chart)

Problem 4

The stopecay Co sells an electric toothbrush for $25. Its sales have averaged 8,000 units per month over the last year. Recently, it's closest competitor, Decayfighter, reduced the price of its electric toothbrush from $35 to $30. As a result, Stopcay's sales declined by 1500 units per month.

A - What is the arc cross elasticity of demand between Stopcays' toothbrush and Decayfighter toothbrush? What does this indicate about the relationship between the two products?
B - If stopdecay knows that the arc price elasticity of demand for its toothbrush is -1.5 what price would Stopdecay have to charge to sell the same number of units as it did before the Decayfighter price cut? Assume that Decayfighter holds the price of its toothbrush constant $30.
C - What is Stopdecay's average monthly revenue form the sale of electric toothbrushes before and after the price change determined in part (b)?

Problem 5

KROM-FM is currently contemplating a T-shirt advertising promotion. Limited sales data from a new T-shirt shops marketing a prototype of the KROM design indicate that

Q-1200 - 200P

Where Q is T-shirt sales and P is price

a. How many tshirts could KROM sell at $4.50 each?
b. What price would KROM have to charge to sell 900 tshirts
c. At what price would tshirt sales equal zero?
d. How many tshirts could be given away?
e. Calculate the point price elasticity at a price of $2.00

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Solution Preview

Problem 2.

Own price elasticity of demand is a measure of the percentage change in quantity demanded caused by a percentage change in price. Thus it is calculated as % change in demand/ % change in price. Because the demand function is an inverse relationship between price and quantity the coefficient of price elasticity will always be negative.

Arc elasticity is the range along the demand curve. It is calculated as:
change in quantity/change in price x average P/average Q

Cross price elasticity of demand is a measure of the percentage change in quantity demanded caused by a percentage change in the price another product. Thus it is calculated as % change in demand product A/ % change in price product B.

First, calculate the average quantity and price for X for periods 1 and 2:

220+ 80/ 2 =150
15+25/2 =20

Then calculate arc elasticity:
s = -140 / ...

Solution Summary

Calculating elasticities in a competitive marketplace for managerial decision making.