suppose Y=100 is fixed,suppose the consumption function is c(Y-T)=20+M(Y-T), where M is constant between 0&1,suppose the investment function is I(r)=30-50r,suppose we leave G&T as un specified constant.drive equilibrium interest rate&predict effect of increase i G on r
I'll do you a favor and answer your question.
The sufficient reoccurring M factor is 4, and Y:T radius is 3-5=-2. With that we get our 'supposed' main rate and predicament. G=i+r, and if R=M as shown in equation #1, and the Y:T ratio is also I = 6, then that means the ending 'i G on r' is 10.
The ending factor is 10.
To find the equilibrium interest rate (r), we need to determine the point where the demand for funds equals the supply of funds. In this case, the demand for funds comes from investment (I) and the supply of funds comes from saving (S). The equation for saving is given by:
S = Y - C(Y - T)
Where:
- S = Saving
- Y = Income
- C = Consumption
- T = Taxes
Since Y = 100 is fixed and given, we can substitute it into the equation:
S = 100 - C(100 - T)
Now, let's calculate consumption (C) using the given consumption function:
C(Y - T) = 20 + M(Y - T)
Substituting Y = 100 and rearranging the equation:
C(100 - T) = 20 + M(100 - T)
C = (20 + M(100 - T))/(100 - T)
Now we can substitute this value of C into the saving equation:
S = 100 - (20 + M(100 - T))/(100 - T)
We also know that S equals investment (I), so we can equate these two to solve for the equilibrium interest rate (r):
I = S = 100 - (20 + M(100 - T))/(100 - T)
Given the investment function:
I(r) = 30 - 50r
We can substitute this into the equation:
30 - 50r = 100 - (20 + M(100 - T))/(100 - T)
Now, we can solve for r by simplifying and rearranging the equation:
50r = 70 + (20 + M(100 - T))/(100 - T)
r = (70 + (20 + M(100 - T))/(100 - T))/50
This equation gives us the equilibrium interest rate (r) as a function of M, T, and other constants.
Now, let's consider the effect of an increase in G (government spending) on r. An increase in G will increase the demand for funds, resulting in a shift in the demand for funds curve to the right. As a result, the equilibrium interest rate (r) will increase because there is more competition for the available funds.
It's important to note that this explanation assumes other factors, such as the money supply and inflation expectations, remain constant.