Question

A person has $250 to spend on two goods (x and y) whose respective prices are $2 per unit and $5 per unit.

1. Draw the budget line showing all the different combinations of the two goods that can be bought with the given budget.
2. What happens to the budget line if the budget (money available to spend) increases by 100%.
3. What happens to the budget line if the price of good x decreases by 50%?
4. What happens to the budget line if the price of good y increases to $10 per unit?

3. [National Income Model] 30 points

Let

AE =C+I+G+NX

where AE is the aggregate expenditure, C is the consumption function, I is investment,

G is government expenditure and NX is the net export. Given

C =100+0.65Y

where Y is the national income and

1. =100, G=100+0.10Y, NX =0

1. Graph the consumption function withY on the horizontal axis andC on the vertical axis.
2. Graph the aggregate expenditure function with Y on the horizontal axis and AE on the vertical axis.
3. Find the equilibrium level of income without using graph analytically.
4. Find the equilibrium level of consumption C.

Answer 1

The budget line is income = Px*X + Py*Y

Here the budget line is 250 = 2x + 5y

a) if the consumer spent all income on good x then he can buy 125 units (250/x). This is the x intercept (125, 0). Similarly if the consumer spent all income on y he can buy 50 units (250/5). This is the y intercept (0,50). Joining the two points so obtained gives the consumer's budget line wherein he can buy all the consumption bundle below the line as well as those on the line (the shaded area)

b) The income increases by 100% means there is an increase of 250 in the income

The new budget line will be 500 = 2x + 5y

Using the same logic as above we find the x intercept to be 250 (500/2) and the y intercept to be 100 (500/5) now. Joining these two new intercepts gives the new budget constraint as shown (the orange line). As is evident from the figure the budget line in this case will shift parallelly outwards and the quantities that can be purchased of each good also increases by 100%

c) The price of x decreases by 50% means there is a decline of 1 dollar in the price

The new budget line will be 250 = x + 5y

Using the same logic as above we find the x intercept to be 250 (250/1) and the y intercept remains the same which is 50 (250/5). Joining these two new intercepts gives the new budget constraint as shown (the orange line). As is evident from the figure the budget line in this case will shift outwards but not parallelly as only good x has become cheaper so only the x intercept moves outwards while the y intercept remains the same

d) The price of y increases to 10 dollars. Y has become costlier

The new budget line will be 250 = 2x + 10y

Using the same logic as above we find the x intercept remains the same which is 125 (250/2) and the y intercept now is 25 (250/10). Joining these two new intercepts gives the new budget constraint as shown (the orange line). As is evident from the figure the budget line in this case will shift inwards but not parallelly as only good y has become costlier so only the y intercept moves inwards while the x intercept remains the same

Question 3)

a) C = 100 + 0.65 Y

We graph this function by first finding the value of C when Y is 0

If Y = 0 then C = 100

The slope (dC/dY) of this line is 0.65 so we plot an upward sloping line from (0,100) with a slope of 0.65. The graph looks like the one shown below

b) AE = C+ I +G +NX

Given C =100+0.65Y, I=100, G=100+0.10Y and NX =0

Putting these values in AE we get

AE = 100+0.65Y + 100 + 100+0.10Y + 0

On simplification

AE = 300 + 0.75Y

We graph this function by first finding the value of AE when Y is 0

If Y = 0 then AE = 300

The slope (dAE/dY) of this line is 0.75 so we plot an upward sloping line from (0,300) with a slope of 0.75. The graph looks like the one shown below

c) Equilibrium level of income is at the point where

Y = C + I + G + NX

Given C =100+0.65Y, I=100, G=100+0.10Y and NX =0

Putting these values in the equilibrium equation we get

Y = 100+0.65Y + 100 + 100+0.10Y + 0

On simplification

Y = 300 + 0.75Y

0.25Y = 300

Y = 300/ 0.25

Y = 1200

This means the equilibrium level of income is 1200

d) The equilibrium level of C is the value of consumption at the equilibrium level of income

From part c the equilibrium level of income is 1200 and the consumption function is C = 100 +0.65Y

Putting equilibrium Y in Consumption function we get

C = 100 + 0.65 * 1200

C = 880

Therefore the equilibrium level of consumption is 880

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