Homework 7

Homework 7

Introduction

The following assignment will answer the questions regarding the profit maximization, demand and supply, price elasticity and dead weight loss situations faced by the firms in an economy. The answering of the following questions will help in understanding the concept and application of economics in different scenarios.

a) Profit Function is equal to Total Revenue minus Total Cost. The Profit function derived will be:

Profit = TR - TC

Profit = (22Q - 1.7 Q^2) - (6 + 3.5 Q + 0.55 Q^2)

Therefore, Profit Function will be 2.25 Q^2 + 18.5Q - 6

b) The profit at maximized output will be at

Q = 0; P = 2.25 (0^2) + 18.5 (0) - 6, P= (-6)

Q = 1; P = 2.25 (1^2) + 18.5 (1) - 6, P= 14.75

Q = 2; P = 2.25 (2^ 2) + 18.5 (2) - 6, P = 40

Thus the profit function shows that as the output increases the profit function also increases.

c) Q = 0; P = 2.25 (0^2) + 18.5 (0) - 6, P= (-6)

Q = 1; P = 2.25 (1^2) + 18.5 (1) - 6, P= 14.75

Q = 2; P = 2.25 (2^ 2) + 18.5 (2) - 6, P = 40

Price elasticity of demand is calculated by using the mid-point formula which is:

Price Elasticity of demand = % change in quantity / % change in Price

Price Elasticity of Demand = (952 - 1012 / 1012) / (8.45 -6.75 / 6.75)

Price Elasticity of Demand = - 0.06 / 0.25

Price Elasticity of Demand = - 0.24

If the price elasticity of demand is more than one it will be termed as elastic but if the price elasticity of demand is lesser than one then it will be called inelastic. A product or service having a demand inelastic means that a change in quantity will have a large amount of change in price.

a) The demand function as p = f (Q) means, p = - Q / 480. Thus showing the relation of price and quantity on demand that if quantity decreases demand will increase.

b) Estimated Equation on interest rate 10% will be Q = -480 P -100000

c) Estimated Equation on interest rate 6% will be Q = - 480 P - 600000

The return to scale for the following production functions will be:

Q = 0.3x + 6y + 17z, assuming x = 200, y = 100 and z = 300

Q = 5760

Q = 0.8 L^2 + 3.7 LK +3.7K^2, assuming L= 100 and K = 300

Q = 452,000

Q = 5A + 5B + 3.8AB, assuming A = 200 and B = 300

Q = 230500

Q = 4L ^ 0.6 K ^0.4, assuming L = 200 and K = 200

Q = 129.4

The minimum efficient scale (MES) of the two cost curves will be:

5800 + 1555Q + 0.008Q^2 = 1080 + 150Q + 0.009Q^2

TC = 4720 + 1405Q - 0.001Q^2

Q = 0 and Q = 1405000

Q = 2800 and P = ( 2800 -6800 / -1.8)

Consumer dead weight loss will be = 2,222

Producer dead weight loss will be P ...