Question

Question 2 a) Differentiate the following function y = 2x3 - 6x-2 - 4x + 10    b) You invest a K1000 once is a savings account offering 8 interest per annum for 5years. If the interest is compounded, how much would be the value after 5 years. c) If a business currently sells 10,000 units of its product per month at $10 per unit and the demand for its product has a price elasticity of -2.5, a rise in the price of the product to $11 will: d) Write brief notes on each of the following; I. Compensatory Theory of Economic Profits (2) Producer-Producer rivalry (3) Consumers surplus .

Answer 1

a). The function is defferentiated in the image below.

b). The investment amount in saving account = 1000 (say dollar as unit)  

Given interest rate = 8% per annum for 5 years.

We have to find the compound value of 1000 at interest rate of 8% compounded anuualy for 5 years.

The formula for finding compound value of an investment amount through coumpound interest rate is given by:

A = P ( 1 + r/n)^

where, A = The future value of investment amount, which we have to find using compound formula.

P= principle amount for investment, which is 1000

r = interest rate which is 8%

t = total duration of interest being applied/ offered on investment amount, which is 5 years.

n = coumpound period, which is annualy in this question and so is 1.

Therefore we have;

P= 1000, r= 8%, t= 5, n= 1 and A = ?

Using above formula now we find the compound value of investment amount of 1000 at 8% interest per annum coumpounded annualy for 5 years;

A = P ( 1 + r/n)^

A = 1000 (1+ 8%/1)^1*5

A = 1000 (1 + 8/100)^5

A = 1000 (1+ 0.08)^5

A = 1000 (1.08)^5   A = 1000 ( 1.4693280)

A = 1469.3280

Hence, the compound/ future value of investment amount of 1000 at 8% interest rate per annum after 5 years is 1469.328 dollar.

c). Quantity sell = 10,000 units per month

Price of product sell = $10 per unit

Price elasticity of demand for the product = -2.5

Price rises to $11

Change in price = New price (P2 )- old price (P1) = $11 - $10 = $1

Formula for price elasticity of demand = percentage change in quantity / percentage chnage in price

Ed = (Change in quantity/chage in price) * old price / old quantity

Ed = [ {New quantity ( Q2)  - old quantity (Q1)} / {New price (P2 )- old price (P1)} ] * $10/ 10,000

  Ed  = [{ Chnange in quantity (Q) / $1} * 10/ 10,000 ]

-2.5= Q * 1/1000

-2.5 * 1000 = Q  Q = -2.5* 1000 = -2500

  Q = {New quantity ( Q2)  - old quantity (Q1) }

-2500 = Q2 - 10,000    Q2 = 10,000 -2.500 = 7500

Therefore, new quantity being demanded after the price increased by $1 at price elasticity of demand of -2.5 is 7500 units. Hence, with the increase in price quantity of product demanded has decreased.

d). Compensatory Theory of Economic Profits: Frank Knight argued about compensatory theory of economic profit also known as risk or uncertainty bearing theory. According to Frank Knight, economic profit is the reward to enterentrepreneur of bearing non-insurable risks and uncertainties. It is a deviation arising from uncertainty. In the business operation, other factors mainly land labbour and capital have con­tractual agreements of payment for their services – wages, rent and interest, but for the enterpreneur, the left over revenue after paying compensation to these factors is the economic profit.

Producer - producer rivalry: As the term itself clearly suggest, that rivalry or competition between the producers or firms in a market may exit. With the existance of competition each producer will try to cover most of market by selling more of the good. This possible when the producer will reduce the price of good, as the Marshallian law of demand suggest. Thus rivaly between producers increase the competition among the producers in the market and the price of product decreases.

Consumer surplus: It is also called consumer welfare. It is the difference between the price that consumers are willing to pay for a product and what they actually pay for it. On the diagram of demand and supply, it's the area above the equillibrium market price for product and below demand curve, which mainly forms a shape of a triangle. So using the formula for area of trinagle we calculate consumer surplus.