Question

Joe's income is $300. He can buy 2 goods – Food and Shelter. a. (5 points) Write the budget constraint and draw the budget line when the price of food (F) is $5 per unit, and the price of shelter (S) is $100. b. (5 points) Write the budget constraint and draw the budget line when the price of food increases to $10 per unit, and the price of shelter stays the same at $100. c. (5 points) Calculate the opportunity costs of food in parts (a) and (b). Do they increase, decrease, or stay the same?

Answer 1

The budget constrain is how much of each good can Joe's buy and it's given by:

Income = P_f * Q_f +P_s * Q_s  

P_f = Price_of_Food

Q_f = Quantity_of_Food

P_s = Price_of_Shelter

Q_s = Quantity_of_Shelter

In case a):

300 = 5*Q_f(a) + 100*Q_s

in case b):

300 = 10*Q_f(b) + 100*Q_s

To draw each line, you can make a graphic in which the x axis is Q_s and y axis is Q_f

set Q_f = 0 and solve for Q_s which gives => Q_s = 3 so, in the x axis the line will start in Q_s = 3

the same, and solve for Q_f and it'll give =>

Q_f(a) = 60

Q_f(b) = 30

So, from the start in x axis in Q_s = 3 you draw the line (a) to the y axis Q_f(a) = 60 and you draw the line (b) to the y axis Q_f(b) = 30

To get the oportunity cost you have to divide the cost of what is given up (food) by what is gained (shelter).

Oportunity_Cost_Food(a) = 5/100 = 0.05

Oportunity_Cost_Food(b) = 10/100 = 0.10

As you can see, the oportunity cost of food increase