Assume a consumption function that takes on the following algebraic form: C = $100 + .8Y. Assume that Y = $1000 what is the level of consumption at this income level.
C = $100 + .8($1000) = $100 + $800 = $900.
1. Using the above figure calculate the marginal propensity to consume between the aggregate income levels of $80 and $100. Also explain why this consumption function is linear.
The marginal propensity to consume is equal to $15/$20 = .75. The consumption function is linear because the marginal propensity to consume is constant and therefore the slope is the same throughout all income levels.
2. Assume consumption is represented by the following: C = 400 + .75Y. Also assume that planned investment (I) equals 100.
(a) Given the information, calculate the equilibrium level of income.
C= 400 + .75Y
By substituting (2) and (3) into (1) we get:
There is only one value of Y for which this statement is true. We can find it by rearranging terms:
(b) Given the information, calculate the level of consumption and saving that occurs at the equilibrium level of income.
To get value of consumption at equilibrium, simply plug in Y = 2000 in the consumption function to get:
C= 400+ 1500
S= Y- C
C = 1900 and S = 100
(c) Suppose planned investment increases by 100. Calculate the new equilibrium level of income. Given your answer, what is the size of the multiplier for this economy?
Y increased by 400 as a result of the 100 unit increase in I. The multiplier is, therefore, 4.
(d) Will the level of saving and consumption change as the economy adjusts to this change in planned investment? Explain.
Consumption (C) will rise as Income (Y) rises. Savings will also rise as Income (Y) rises.
3. Draw a graph of a "planned investment function" (with I on the vertical axis and Y on the horizontal axis) assuming that I is independent of aggregate income. Comment on the realism of this function.
The investment function assumes that investment will be the same no matter what the level of aggregate income is. This is not likely to be very realistic. We would assume that as aggregate income rises firms would be more inclined to invest and vice versa.
5. Algebraically derive the value of the multiplier assuming the basic form of the consumption function as C = a + bY where "a" is autonomous consumption and "b" is the marginal propensity to consume. You may assume a two-sector private economy.
Since Y = C + I we can write Y = a + bY + I.
This equation can be rearranged as
Y - bY = a + I
Y(1-b) = a + I
We can then solve for Y in terms of I by dividing through by (1 - b):
Y = (a + I) (1/1 - b)
Now we can see that an increase in I will increase Y by
(Y = (I x (1/1 - b)
Since b ( MPC, the expression becomes
(Y = (I x 1/(1 - MPC)
Therefore, the multiplier is 1/1 - MPC or 1/MPS.
6. List and explain five factors which affect the investment in an economy.
• Business confidence and expectations about the future • levels of growth of demand
• technical change and product innovation
• the real rate of interest tax provisions
7. List and...
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