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Assume that GDP (Y) is 5,000. Consumption (C) is given by the equation C = 1,200 + 0.3(Y – T) – 50 r, where r is the real interest rate. Investment (I) is given by the equation I = 1,500 – 50r. Taxes (T) are 1,000 and government spending (G) is 1,500. a. What are the equilibrium values of C, I, and r?

Respuesta :

michaellj973

Answer:

Explanation:

Code

from sympy import symbols, Eq, solve

# define the symbols

Y, C, I, r, T, G = symbols('Y C I r T G')

# given values

Y_val = 5000

T_val = 1000

G_val = 1500

# equations for C and I

C_eq = Eq(C, 1200 + 0.3*(Y - T) - 50*r)

I_eq = Eq(I, 1500 - 50*r)

# substitute the given values into the equations

C_eq_sub = C_eq.subs({Y: Y_val, T: T_val})

I_eq_sub = I_eq.subs({Y: Y_val, T: T_val})

# solve the equations for C and I

C_val = solve(C_eq_sub, C)[0]

I_val = solve(I_eq_sub, I)[0]

# equilibrium condition: Y = C + I + G

equilibrium_eq = Eq(Y, C + I + G)

# substitute the values of C, I, and G into the equilibrium equation

equilibrium_eq_sub = equilibrium_eq.subs({C: C_val, I: I_val, G: G_val})

# solve the equilibrium equation for r

r_val = solve(equilibrium_eq_sub, r)[0]

C_val, I_val, r_val

Executed Code Output

(2400.0 - 50.0*r, 1500 - 50*r, 54.0 - 0.01*Y)  

Code

# substitute the given value of Y into the equation for r

r_val_sub = r_val.subs(Y, Y_val)

# substitute the value of r into the equations for C and I

C_val_sub = C_val.subs(r, r_val_sub)

I_val_sub = I_val.subs(r, r_val_sub)

C_val_sub, I_val_sub, r_val_sub

Executed Code Output

(2200.00000000000, 1300.00000000000, 4.00000000000000)  

The equilibrium values are as follows: Consumption (C) is 2200, Investment (I) is 1300, and the real interest rate (r) is 4.

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