Economics Lesson
Question 1
(a)
We have U = F
1/2
C
1/2
Budget Equation will be: P
F
F + P
C
C = Income
i.e. F + C = 100
To Find the optimal demand, we need to equate MRS with price ratio
MRS = (dU/dF)/(dU/dC) = ((1/2)F
-1/2
C
1/2
)/ ((1/2)F
1/2
C
-1/2
) = C/F
Price Ratio = P
F
/P
C
= 1 / 1 = 1
MRS = Price Ratio Gives:
C/F = 1
i.e. C = F
Substitute C = F in Budget Equation
F + F = 100
2F = 100
F = 50
Since C = F, Thus, C = F = 50
So, (C, F) = (50, 50)
SO, Consumer will buy 50 units of each.

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(b)
Since 200 units of food is free, which would have otherwise costed 1*200 = 200
This is equivalent to giving income of 200 but with restriction that only food can be
bought with it.
So, if the quantity of food is greater than 200, we can treat 200 as additional Income
i.e. F + C = 300
if
F >= 200
For remaining portion, the budget constraint will be same as before i.e. F + C = 100
We can draw this as follows:
Now, using the new constraint:
F + C = 300
And Using MRS = Price Ratio condition, we get: F = C
Substituting in Budget, we get:
C + C = 300
2C = 300
C = 150
F = C = 150
But since the subsidy is on food and not on composite goods, so, C cannot exceed 100 i.e.
max value of C can be: Income/Price of C = 100/1 = 100

But he wants to purchase C = 150 which is not possible
SO, C will be restricted to 100 and rest of the income will be spent on food i.e. if C = 100,
we get:
F + 100 = 300
F = 200
So, (F, C) = (200 , 100) is the new demand
(c)
This can be represented graphically as follows:
Initial indifference curve was much lower than the new one. Thus, the household is
better off with subsidy
Initially Utility was, U = 50
1/2
50
1/2
= 50
New Utility, U = 200
1/2
100
1/2
= 141.42
Household is better by: 141.42
–
50 = 91.42 units of utility
Here, we have assumed 1 utility = 1$. Thus, household is better off by 91.42 dollars

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Question 2
The budget line takes the form:
P
Gasoline
*Q
Gasoline
+ P
Other_Goods
*Q
Other_Goods
= Income
Suppose income was initially 10000 and Price of other goods was 1, we get the budget equation
as:
1*G + 1*C = 10000
i.e. G + C = 10000
After price hike and rise in income, budget equation becomes:
2G + C = 11000
Initially, the consumer was spending following on Gasoline: Quantity * Price = 1000*1 = 1000
After the hike, the consumer will be spending following on same quantity of Gasoline:
Quantity *Price = 1000*2
= 2000
Excess money required to buy this: 2000
–
1000 = 1000
Excess money he got = 1000

- Spring '14