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Elementary Calculus

E1.(6 pts) Which of the following goods are likely to have elastic demand, and which are unlikely to have inelastic demand? Explain.

Home heating, oil, water and heart medication have inelastic demand because they are essential products that will not have a change in demand in case the prices are increased. Pepsi, chocolate and oriental rugs have elastic demand because they are products that are not essential. they also have a variety of alternatives so the increase in price will lead to decrease in demand.

E2. (4 pts) If the price of a good increases by 8% and the quanitity demanded decreases by 12%, what is the price elasticity of demand? Is it elastic, inelastic or unitary elastic?

Price Elasticity of Demand = Percentage Change in Quantity Demanded

Percentage Change in Price

= 12%

8%

= – 1.5

E3. (10 Pts) John Advertises to sell chocolate bars for €4 a dozen. He sells 50 dozen, and decides that he can charge more. He raises the price to €6 a dozen and sels 40 dozen. What is the elasticity of demand? Assuming that the elasticity of demand is constant, how many would he sell if the price were € a box?

Point A: Price (P1) = €4 Quantity (Q1) =50 Dozen

Point B: Price (P2)= €6 Quantity (Q2)=40 Dozen

Elasticity of Demand =(Q2-Q1)/[(Q2+Q1)/2]

(P2-P1)/[(P2+P1)/2]

= (40-50)/[(50+40)/2]

(6-4)/[(6+4)/2]

= -0.4E4. (5 pts) Suppose at a price of $10 the quantity demanded is 100. When price falls to $8, the quantity demanded increases to 130. The absolute value of the price elasticity of demand between the prices of $10 and $8 is approximately:

Price elasticity of demand=(Q2-Q1)/[(Q2+Q1)/2]

(P2-P1)/[(P2+P1)/2]

=(130-100)/[(130+100)/2]

(8-10)/[(8+10)/2]

=0.22

E5. (15 pts) All businesses face a similar question: What price for their product will generate the maximum profit? The answer is not always obvious: Raising the price of something often has the effect of reducing sales as price- sensitive consumers seek alternatives or simply do without. For every product, the extent of that sensitivity is different. The trick is to find the point for each where the ideal tradeoff between profit margin and sales volume is achieved.

The average number of fans attending the home soccer games are not enough to occupy even half the stadium. Increasing the current charges whic is $8 will have a negative effect on the fans coming to watch the game. this is because the service offered is not essential and will most likely be affected by changes in price. When the price goes up, the stadium will experience a reduction in the number of fans coming to watch the game. the best option will be to reduce the price which will capture the attention of those fans who initially did not have the money to attend the games. the increase in demand will increase the capacity of people ttending the game thus increasing the amount of money collected through tickets. The profits made will be higher when the prices are reduced as compared to high prices that lead to a decrease in demand. There will also be an increase in revenue because the services is highly respponsive to price. A fall in the prices causes the demand ti increase by a certain percentage at the same time increasing the total revenue.