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Maths Assignment

Question 1

  1. The Atlantis tribe could not have been able to produce 800 bushels of wild oats and 5,000 kilograms of the simultaneously because their productivity does not allow such a combination. As such, there would be no such point on the production possibility frontier (Elberse & Eliashberg, 2003).
  2. The marginal opportunity cost of increasing annual the annual output of wild oats from 300 to 500 could have been 1,000 kilograms of fish.
  3. The marginal opportunity cost of increasing annual output of wild oats from 625 to 825 could have been 3,000 kilograms of fish.
  4. The marginal opportunity costs of the 200 batches are different because of the difference in productivity of the people based on the nature of product to be produced.

Question 2

  1. Based on the information provided form the graph, the equilibrium price and quantity of the Brazilian Coffee beans stands at $3.00 and 4,000 kilograms respectively.
  2. The table below shows the combined total quantity of the Brazilian Coffee beans that is being demanded by both the Brazilians and Canadians

 

Price of Brazilian Coffee beans

Canadian Quantity of Brazilian Coffee beans demanded

Brazilian Quantity of Brazilian Coffee beans demanded

Total Brazilian Coffee Demanded

(per pound)

(pounds)

(pounds)

(pounds)

$4.00

1,000

1,000

 2,000

$3.50

2,500

2,500

 5,000

$3.00

3,000

4,000

 7,000

$2.50

5,000

5,000

 10,000

$2.00

5,500

7,000

 12,500

 

  1. Based on the data provided by the supply schedule and the combined demand schedule, the new price at which the Brazilian coffee growers will be able to sell the coffee beans is $ 3.50
  2. Considering that the coffee growers are selling to both the Brazilians and the Canadians, the local market of the coffee beans will be the based on the original price determined by the local demand alone.
  3. Considering that the coffee beans are being consumed locally and internationally, the quantity consumed by the Brazilians will be determined by the combined demand schedule of Brazilian and Canadian demand.

Question Three

  1. Based on the diminishing levels of satisfaction, it can be inferred that Jane is not maximizing her utility. Instead, she is reducing it.
  2. The Law of Diminishing Marginal Utility states that an additional unit of the same product has a lesser level of satisfaction. However, now that Jane is utilizing both products simultaneously, it is not advisable to buy one less chicken sandwich and one more fry. The purchase combinations cannot be supplemented by adding a unit of one on the cost of the other since it will not maximize utility (Elberse & Eliashberg, 2003).
  3. Even if Jane switches to just one more fry, the utility will not be maximized because the level of satisfaction continues to decrease with increased consumption of the same product.
  4. The law of diminishing marginal utility shows that any additional consumption of the same product has lesser satisfaction levels which imply that even if Jane substituted fries for chicken, the utility derived from the sandwich will increase.

Question Four

a. The price elasticity of demand is a term used to refer to the relationships that exists between the price of a product and the quantity demanded at a specified time.

midpoint
elasticity

=

(B2 - B1)

 

(B2 + B1)/2

÷

(A2 - A1)

 

(A2 + A1)/2

As such,

midpoint
elasticity

=

(84 - 70)

 

(84 + 70)/2

÷

(700 - 600)

 

(600 + 700)/2

Price elasticity of demand for the berries is 1.18

 

             

b. The monthly average total revenues for year 107 and year 108 are shown in the table below.  The slight increase in monthly average total revenue shows that the price elasticity of demand impacted higher on the revenues realized (Hughes, Knittel & Sperling, 2006).

 

Year (WBCE)

Monthly barrels of gosum berries demanded

Price per barrel

Monthly average total revenue

107

700

$70

$49,000

108

600

$84

$50,400

 

 

Change in

average total monthly revenue

$1,400

 

c. Based on the positive result on the price elasticity of demand, the above difference could have been predicted as an increase since it implies increased demand and hence higher revenue (Hughes, Knittel, &Sperling, 2006).

Question Five

a. True. The increase of the Altair chariot price by 20% will result in a decrease in the quantity demanded by 60% due to the price elasticity of 3.

b. False. Increasing the consumers incomes will not directly lead to increased prices but will instead lead to increased demand in the long run.

Question Six

Part a

midpoint
elasticity

=

(B2 - B1)

 

(B2 + B1)/2

÷

(A2 - A1)

 

(A2 + A1)/2

As such,

midpoint
elasticity

=

(20 - 10)

 

(20 + 10)/2

÷

(900 - 800)

 

(900 + 800)/2

The price elasticity of demand after a shift of prices from $10 to $20 is 5.67 which imply a positive elasticity.

Part b

midpoint
elasticity

=

(B2 - B1)

 

(B2 + B1)/2

÷

(A2 - A1)

 

(A2 + A1)/2

As such,

midpoint
elasticity

=

(80 - 70)

 

(80 + 70)/2

÷

(300 - 200)

 

200)/2

The price elasticity of demand after a shift of prices from $70 to $80 is 0.33 which imply a positive elasticity though it has reduced.

Part C: The price elasticity of demand changes along the demand curve because of the changes in the prices of the product when compared to the corresponding demand (Elberse & Eliashberg, 2003).

Question Seven

  1. At the initial point of consumption, a consumer always gets maximum satisfaction. As such, the Matilda is not maximizing her utility since it has shown a decreasing curve.
  2. In order to move closer to optimum level of utility, Matilda cannot achieve this by increasing her consumption.
  1. Matilda should not purchase one less music download and one more video download in order to move achieve optimum utility level. Optimum utility is only achieved at the initial point of consumption.
  2. Matilda should not purchaseone more music download in order to move achieve optimum utility level. Optimum utility is only achieved at the initial point of consumption.

Question Eight

  1. At the cost of $3, Brandon can afford to buy 9 movie rentals and have 1 consumer surplus.
  2. At the cost of $5, Brandon can afford to buy 5 movie rentals and have 3 consumer surpluses.
  3. If the annual subscription is fixed at $25, Brandon will be able to download 8 movie rentals and receive unlimited consumer surpluses.
  4. The demand for Brandon is 8 movie rentals which mean that he will able to download 8 movie rentals and receive unlimited consumer surpluses.
  5. Based on the demand shown by Brandon, the average price that could be charged is $28.

Question Nine

Marginal utility is the added satisfaction that is derived from consumption of an additional unit of a product or service. With respect to magazines and newspapers, the vending machines are designed in such a way that they offer maximum satisfaction since the product satisfies the same need. However, the sodas and snacks machines are designed to satisfy the specific need of the consumer based on preference and demand (Hughes, Knittel, &Sperling, 2006).

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