Question

In: Economics

Consider the following equations that describe desired consumption, desired saving, taxes, and the demand for money...

Consider the following equations that describe desired consumption, desired saving, taxes, and the demand for money of a hypothetical economy.

Cd = 200+0.75(Y-T)-500r

Id = 250-500r

T= 20+0.4Y

Md/P = 0.5Y -250(r+πe)

The values of other variables are: Y=1000, G=200, πe = 0.1, the nominal money supply=10,000.

(a) Find the general equilibrium values of the real interest rate, consumption, investment, and price level.

(b) Find the size of government budget deficit or surplus?

(c) Derive the equation that describes the IS curve without substituting for Y (Hint: For any level of output, Y, find an equation that gives the real interest rate, r, that clears the goods market. This involves writing the goods market equilibrium condition and solving for r (as a function of Y and other variables).

(d) Derive the equation that describes the LM curve without substituting for Y (Hint: For any level of output, Y, find an equation that gives the real interest rate, r, that clears the asset market. This involves writing the goods market equilibrium condition and solving for r (as a function of Y and other variables).

(e) Describe what the effects of increasing G would be on the general values of the real interest rate, consumption, investment, and price level.

Solutions

Expert Solution

In an economy, at equilibrium, Y=AD, where Y is the level of output and AD, is the aggregate demand

AD= C(YD)+I+G

The components of AD is the consumption investment and government expenditure

AD = Cd + Id + G

Consider the following hypothetical economy.

AD = 200+0.75(Y-T)-500r + 250-500r + 200

      = 200+0.75(Y-20-0.4Y)-500r + 250-500r + 200

      = 200 +0.75Y -15 – 0.3Y -1000r +250 +200

     = 635 + 0.45Y -1000r

At equilibrium, Y=AD

Y = 635 + 0.45Y -1000r

Y – 0.45Y = 635 -1000r

0.55Y = 635 – 1000r

Putting the value of Y we get,

0.55(1000) = 635 – 1000r

1000r = 635 – 550

r = 85/1000

r = 0.08

This is the general equilibrium values of rate of interest.

Cd = 200+0.75(Y-20-0.4Y)-500r

     = 200 -15 +0.45Y – 500r

     = 185 + 0.45(1000) – 500 (0.08)

     = 185 +450 – 40

     = 595

This is the the general equilibrium values of consumption.

Id = 250-500r

   = 250 – 500(0.08)

   = 250 – 40

   = 210

This is the the general equilibrium values of the investment.

At money market equilibrium , MD = MS

Md/P = 0.5Y -250(r+πe)

MS = 10000

10000/P = 0.5Y -250(r+πe)

P = 10000/ [0.5(1000) – 250( 0.08 +0.1)]

   = 10000/ [500-45]

   = 10000/455

= 21.9 = 22(approx)

This is the the general equilibrium values of the price.

(b)

T= 20+0.4Y [ Y=1000 given]

   = 20 + 0.4(1000)

   = 20 +400

   = 420

The size of government budget deficit = Government expenditure – government revenue (Tax)

                                                              = G – T

                                                              = 200 – 420

                                                              = -220

The negative value of government deficit means the government has budget surplus by the amount 220. The revenue of the govt is greater than the expenditure.

(c)

AD= C(YD)+I+G where C is a function of disposable income (Y-T)

AD = 200+0.75(Y-T)-500r + 250-500r + 200

      = 200+0.75(Y-20-0.4Y)-500r + 250-500r + 200

      = 200 +0.75Y -15 – 0.3Y -1000r +250 +200

     = 635 + 0.45Y -1000r

At equilibrium Y=AD

Y = C(YD)+I+G

Y = 635 + 0.45Y -1000r

Y – 0.45Y = 635 -1000r

0.55Y = 635 – 1000r

1000r = 635 – 0.55Y

.r = 0.635 – 0.0005Y

This is the equation of the IS curve.

(d)

At money market equilibrium, MD = MS

Md/P = 0.5Y -250(r+πe)

MS = 10000

10000= 0.5Y -250(r+πe)

250(r + 0.1) = 0.5Y -10000

250r = 0.5Y- 10020.5

.r = 0.002Y – 40.082

This is equation of LM curve.

(e)

G is a component of AD curve. If G increases, it will affect the AD curve. The curve will shift upward because increasing G will affect the coefficient of the curve. Thus there is a shift in the IS curve. IS curve shifts to rightward as a result, the rate of interest and the level of output both increases.

Consumption will also rise.

Again investment is a function of rate of interest. There is a negative relation between the rate of interest and the investment. Increase in r implies fall in investment.

Increase in rate of interest induces to rise in price level P.


Related Solutions

Consider the following equations that describe a closed economy with no government. Assume consumption is represented...
Consider the following equations that describe a closed economy with no government. Assume consumption is represented by the following: C = 200 + 0.9Y. Also assume that planned investment (I) equals 300. Obtain the saving function for this economy. What are the marginal propensity to save (MPS) and marginal propensity to consume (MPC)? Write the equation for the planned aggregate expenditure. Find the equilibrium level of output and calculate the level of consumption and saving that occurs at the equilibrium...
Consider the following economy (with flexible exchange rate system): • Desired consumption: Cd = 300 +...
Consider the following economy (with flexible exchange rate system): • Desired consumption: Cd = 300 + 0.5Y −2000r • Desired investment: Id = 200−3000r • Government purchases: G = 100 • Net export: NX = 350−0.1Y −0.5e • Real exchange rate: e = 20 + 1000r • Full employment: ¯ Y = 900. • Nominal money stock: M = 4354 • Real money demand: L = 0.5Y −200r (f) Using the IS-LM-FE model, evaluate the effects of a rise in...
1. Saving and Investment (a). Consider the consumption expenditure function ? = ?̅ + ?(? −...
1. Saving and Investment (a). Consider the consumption expenditure function ? = ?̅ + ?(? − ?, ?) In each sentence below, fill in the blank with either: increasing, decreasing, or constant. Consumption is a/an __________________ function of disposable income. Consumption is a/an __________________ function of the real interest rate. (b). National saving can be written as ?=?−?−? Substitute the consumption expenditure function from part (a) into this equation. That is, write an equation for saving S that depends on...
Consider the following demand and supply equations. Demand is given by qd = a – bP,...
Consider the following demand and supply equations. Demand is given by qd = a – bP, where qd is the quantity demanded and P is the price. a and b are parameters (constants) Similarly, the supply function is given by qs = d + eP, where qs is the quantity supplied and d and e are constants a. Plot the demand and supply functions. Label the intercepts clearly. b. What is the market equilibrium price and quantity?
1. The following equations describe an economy: Consumption : C = 30 + 0.9YD Investment :...
1. The following equations describe an economy: Consumption : C = 30 + 0.9YD Investment : I = 500 - 14i Government Spending : G = 200 Transfer Payments: TR = 200 Taxes: TA = 0.2Y LM Curve : Y = 2,500 + 100i Re al Money Demand : L = kY - hi Money Suppy : MS = 1,500 Price Level: P = 2 where Y is income, i is the percentage of interest rate, YD is the disposal...
Assume the following set of equations describe the economy of Agriland: Consumption = $100 billion +...
Assume the following set of equations describe the economy of Agriland: Consumption = $100 billion + .6YD YD refers to disposable income Investment = $90 billion Government spending = $70 billion Taxes = .25Y Exports = $65 billion Imports = 0.1Y Calculate the equilibrium level of output for Agriland? (Show formula and calculations) Calculate the multiplier for Agriland. (Show formula and calculations) What is the impact on the equilibrium level of output in Agriland of an increase in government spending...
Consider the following closed Keynesian economy: Desired consumption and investment are given by: Cd = 200+0.8(Y...
Consider the following closed Keynesian economy: Desired consumption and investment are given by: Cd = 200+0.8(Y −T)−500r Id = 200 − 500r. Taxes and government expenditures are given by The real money demand is T = 20+0.25Y G = G=196. Md P = 0.5Y − 250(r + πe). The money supply M = 9890 and the expected inflation πe = 0.10. (a) Derive the equations for the IS and LM curves and show them on a (Y, r) graph. (b)...
Consider a hypothetical economy characterized by the following equations (all variables as defined in class). Consumption:...
Consider a hypothetical economy characterized by the following equations (all variables as defined in class). Consumption: C = 700 + 0.95Y Investment: I=500− 30i Government spending: G=50 Money demand: L(i,Y )=0.75Y − 30i Money supply: Ms/P=400 (a) What is the equation of the IS curve? (b) What is the equation for the LM curve? (c) Solve for the equilibrium values of income (Y) and interest rates (i). (d) Assume that the government engages in expansionary fiscal policy by increasing expenditure...
Consider the following supply and demand equations: Supply: p = 10 + q Demand: p =...
Consider the following supply and demand equations: Supply: p = 10 + q Demand: p = 100 − 2q Show your work as your respond to the following questions.1 (a) What is the market equilibrium price and quantity? (5%) (b) What is the Total Surplus at equilibrium? (5%) (c) The government enacts a price ceiling at ¯p = 50. What is the Total Surplus? D)Calculate the Consumer Surplus under a price ceiling of ¯p = 20. (e) What is the...
Consider the following supply and demand equations: Supply: p = 10 + q Demand: p =...
Consider the following supply and demand equations: Supply: p = 10 + q Demand: p = 100 − 2q Show your work as your respond to the following questions. (a) What is the market equilibrium price and quantity? (b) What is the Total Surplus at equilibrium? (c) The government enacts a price ceiling at ¯p = 50. What is the Total Surplus? (d) Calculate the Consumer Surplus under a price ceiling of ¯p = 20. (e) What is the Deadweight...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT