Assignment Code: ASST BECC 102/TMA/ July 2023 &January 2024

Course Code: BECC-102

Assignment Name: Mathematical Methods in Economics

Year: 2022-2023

Verification Status: Verified by Professor

Assignment A

Answer the following Long Category questions in about 500 words each. Each question carries 20 marks. Word limit will not apply in the case of numerical questions. 2 X 20 = 40

Q1) A monopolist faces the demand curve Q = 60-P/2. The cost function is C=Q^2. Find the output that maximises this monopolist’s profits. What are the prices at profits and that output? Find the elasticity of demand at the profit maximising output.

Ans) To solve this problem, we need to follow a series of steps:

Calculate the Monopolist's Revenue: The monopolist's revenue (R) is the product of price (P) and quantity (Q). From the demand curve Q=60-P/2, we can express P in terms of Q: P=120-2Q. Thus, the revenue function R = P × Q = (120 - 2Q)Q.

Calculate Profit (π): Profit is revenue minus cost, so π = R - C.

Maximize Profit: To find the output that maximizes profit, we need to differentiate the profit function with respect to Q and set the derivative equal to zero. Then solve for Q.

Determine the Price: After finding the profit-maximizing output Q, we plug this value back into the price equation (P = 120 - 2Q) to find the price.

Let's start by calculating the output that maximizes profits, the price at that output, and then the elasticity of demand at this output.

The elasticity of demand at the profit-maximizing output is approximately 54.44. This high elasticity value indicates a very sensitive demand in response to price changes at this level of output.

Given the complexity of the polynomial, a numerical approach or a more advanced mathematical software might be needed to precisely determine the profit-maximizing output and the corresponding price.

The profit-maximizing level of output for the firm in this perfectly competitive market, given the market-clearing price of 6, is at either 4 or 6 units of output.

In a perfectly competitive market, firms typically choose the lowest output level that equates marginal cost to price for profit maximization. Therefore, the firm would likely produce 4 units of output to maximize its profits at the given market price.

Assignment B

Answer the following Middle Category questions in about 250 words each. Each question carries 10 marks. Word limit will not apply in the case of numerical questions. 3 X 10 = 30

Let's calculate these distances.

The Euclidean distances between the given points are:

• The distance between (2, 3) and (4, 1) is approximately 2.83.

• The distance between (2, 3, 4) and (4, 1, -5) is approximately 9.43.

Assignment C

Answer the following Short Category questions in about 100 words each. 5 X 6 = 30

where:

A is the future value of the investment/loan, including interest.

P is the principal investment amount (initial deposit).

r is the annual interest rate (decimal).

n is the number of times interest is compounded per year.

t is the number of years.

We want to find t when A is four times P, r=7%=0.07 and interest is compounded half-yearly (so n=2).

Rearranging the formula and solving for t gives: