Managerial Economics

Practice assignment

Q1) A consumer spends all her income on food and clothing. At the current prices of price of food = Rs. 10 and price of cloth = Rs. 5, she maximizes her utility by purchasing 20 units of food and 50 units of clothing.(Hint: Take food on x-axis and cloth on y-axis)

i)What is the consumer's income?

Answer:

Income is 10*20+5*50=K450

ii)What is the consumer 's marginal rate of substitution of food for clothing at the equilibrium

Answer:

Consumer's marginal rate of substitution of food for clothing at the equilibrium position is

10/5=2

Q2)Ali's budget line relating good X and good Y has intercept of 50 unit of good X and 20 units of good Y. if the price of good X is 12, what is Ali's income? What is the price of good Y? What is then slope of budget line?

Answer:

If a budget line relating good X and good Y has intercept Qx = 20 unit of good X and Qy = 30 units of good Y and Py = $10, then the Ali's income is:

I = Px*Qx + Py*Qy

When the budget line has the intercept Qy = 30 and Py = $10, then I = Px*0 + 30*10 = 300, so the Ali's income is I = $300.

The price of good Y can be found from the income equation in the point of interception with the X-axis:

300 = Px*20 + 10*0,

Px = $15.

The slope of budget line is:

300 = 15*Qx + 10*Qy

10Qy = 300 - 15Qx

Qy = -1.5Qx + 30, so the slope of budget line is -1.5.

Q3) Colgate sells its standard size toothpaste for Rs. 25. Its sales have been on an average 8000 units per month over the last year. Recently, its competitor Sparkle reduced the price of its same standard size toothpaste from Rs. 35 to Rs. 30. As a result Colgate sales declined by 1500 units per month.

i)Calculate the cross elasticity between the two products.

Answer :

ii)What does your estimate indicate about the relationship between the two?

Q4) ) You are given the following marginal utilities of goods X and Y obtained by a consumer. Given that price of X = Rs. 2.5, price of Y = Rs. 1 and income = Rs. 11, find out the optimal combination of goods

No. of unit consumed of a commodity

Marginal utilities of X

Marginal utilities of Y

1

15

10

2

12.5

9

3

10

8

4

7.5

7

5

5

6

6

2.5

5

7

0.5

4

Q5) Suppose the market demand for playing cards is given by the equation

Q = 600 - 100P

Where Q is the no. of decks of cards demand each year and P is the price in Rupee. For a price increase from Rs. 2 to Rs. 3 per deck, what is the price elasticity?

Answer:

There are 4 suits in a deck of cards- Spades, Diamonds, Clubs and Hearts. So, there are 13cardsof each suit. In each suit, there are 9 number cards from 2-10, a Jack, a Queen, a King and an Ace.

So, there are four 8s in a deck of cards, one from each suit. Therefore the probability of getting an 8 from a deck of 52 cards is 8/52 = 3/12 = nearly 15.38%.

Q6) A publishing company plans to publish a book. From the sales data of other publisher of similar books, it works out the demand function for the book as:

Q = 5000 - 5P

Find out

i)Demand curve

ii)Numberof book sold at P = Rs. 25

iii)Price for selling 2500 copies

iv)Price for zero sales

v)Elasticity for fall in price from Rs. 25 to Rs. 20.

Q7) Formulate the demand equations and estimate Qd for P=33 by using the following data:

Qd=P-33

Qs=P-2

Qd = Qs

Price level

Quantity Demand

38

200

36

500

34

800

32

900

30

1000

28

1400