# Demand is determined.

1. A retail store faces a demand equation for Roller Blades given by

Q=180-1.5P,

Where Q is the number of pairs sold per month and P is the price per pair in dollars.

(1)The store currently charges P=$80 per pair. At this price, determine the number of pairs sold.

(2)If management were to raise the price to $100, what would be the impact on pairs sold? On the storeââ?¬â?¢s revenue from Roller Blades?

(3)Compute the point elasticity of demand first at P=$80, then at P=$100. At which price is demand more price sensitive?

A minor league baseball team is trying to predict ticket sales for the upcoming season and is considering changing ticket prices.

(1)The elasticity of ticket sales with respect to the size of the local population is estimated to be about .7. Briefly explain what this number means. If the local population increases from 60,000 to 61,500, what is the predicted change in ticket sales?

(2)Currently, a typical fan pays an average ticket price of $10. The price elasticity of demand for ticket is -.6. Management is thinking of raising the average ticket price to $11. Compute the predicted percentage change in tickets sold. Would you expect ticket revenue to rise or fall?

(3)The typical fan also consumes $8 worth of refreshments at the game. Thus, at the original $10 average price, each admission generates $18 in total revenue for team management. Would raising ticket prices to $11 increase or reduce total revenue? Provide a careful explanation of your finding. (Hint: If you wish, you may assume a certain number of tickets sold per game, say 5,000. However, to answer the question the precise number of tickets need not be specified.)

3. In 1996 the drug Prilosec became the best-selling anti-ulcer drug in the world. (The drug was the most effective available and its sales outdistanced those of its nearest competitor.) Although Prilosecââ?¬â?¢s marginal cost (production and packaging) was only about $ .60 per daily dose, the drugââ?¬â?¢s manufacturer initially set the price at $3.00 per dose----a 400 percent markup relative to MC!

Research on demand for leading prescription drugs gives estimates of price elasticities in the range -1.4 to -1.2. Does setting a price of $3.00 (or more) make economic sense? Explain.

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#### Solution Preview

1. Q=180-1.5P

a) When P = 80, Q = 180 - 1.5(80) = 60. revenue = 80 X 60 = 4800

b) When P = 100, Q = 180 - 1.5(100) = 30 (quantity dropped by 30 units). revenue = 3000. Revenue dropped by $1800.

c) Elasticity = dQ/dP X P/Q.

dQ/dP = -1.5.

At P = 80, elasticity = -1.5 X 80/60 = -2

At P = 100, elasticity = -1.5 X 100/30 = -5.

Since the price is more elastic at P = 100, this price level is also more sensitive to price changes.

2.

a) A population elasticity of 0.7 suggests that if the population increases by 10%, then ticket sales would increase by 7%. From 60,000 to 61,500, the population increases by 2.5%. Thus, this suggests that ticket sales will increase by 1.75%.

b) From $10 to $11, the ...

#### Solution Summary

Demand is determined.

Monte Carlo Simulation:grocery store quantities of fresh produce

A grocery store is trying to determine the optimal amount of fresh produce to have on hand each week.

They have (based on historical figures) determined that their demand for produce is governed by the following discrete random variable.

Winter Summer

Demand Probability Demand Probability

1500 0.1 2000 0.15

2000 0.2 2500 0.2

2500 0.3 3000 0.35

3000 0.25 4000 0.25

3500 0.15 4500 0.05

The cost of the produce is $1 per pound. They can sell it, when fresh, for $3 per pound.

Once It is no longer fresh, the produce is worth only $.10

How much should they order each summer? Each winter?

To do this, simulate each possible order quantity (1500, 2000) many many times.

Then determine which quantity yields the maximum average profit over the 1000 iterations.

Whats your confidence interval for the mean profit?

In other words, whats the 95% confidence interval for the true mean profit.

Find upper and lower bounds.

What is the impact of risk on your decision?

Calculate risk as the standard deviation of the profit.

Enter a trial order quantity (ordered). Then create a random number cell using =RAND()

Simulate demand

The number of pounds sold is the smaller of our order quantity and demand.

You will need to create a data table with 1000 lines for the 1000 iterations.

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