Molly has $6000 in income, the price of food is $2 per unit, and the price of clothing is $4 per unit.

a. Draw Molly's budget constraint with food on the horizontal axis, and clothing on the vertical axis. How do you interpret the slope of her budget line?
b. Molly is now given a $2000 tied grant which must be spent on food. On the diagram from a, graph Molly's new budget constraint.
c. Molly is observed to spend exactly $2000 on food after she receives the grant. Where on the new budget constraint is Molly consuming?
d. Draw the associated indifference curve. Evaluate the following statement: "Molly must be worse off with the tied grant than she would be with an unrestricted grant of $2000 that she could spend as she pleased."

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

Explanation: