Consider the following IS-LM model:  C = 200 + 0.25 YD ; I = 150 + 0.25Y – 1000i ; G = 250 ; T = 200 ; (M/P)d = 2Y – 8000i ; M/P = 1600 Derive the (a) IS-relation and the (b) LM-relation. Solve for the equilibrium (c) real output and (d) interest rate. (e) Solve for the equilibrium values of C and I and verify your equilibrium output by: Y = C + I + G (f) Now suppose that the money supply increases to M/P =  1840. Solve for Y, i, C, I and describe in words the effects of monetary expansion. (g) Set M/P to its initial value 1600. Suppose, that government spending increases to G=400. Summarize the effects of fiscal expansion on Y, i, and C.

Consider an economy in which the consumption, investment and production functions are as follows.C = 90 + 0:7(Y - T)I = 250 - 20r F(K;L) = AK1=2L1=2The capital and labor supply are equal to 100 each, A=10, G = 200 and T = 200. Compute theequilibrium values of output, overall labor income, consumption, public savings, national savings,investment, and the interest rate.Suppose now government spending decreases to G=100 (everything else stays the same). Whathappens to output, consumption, savings, investment and the interest rate? Compute the newvalues for these variables.

The following equations relate to a certain economy, peruse them and answer thefollowing questions.T = 0.75Y (tax rate)L= Y - 100r (Real money demand)M = 300 (Read money supply)C = 200 + 0.25Y d (Consumption function)I = 20 - 10r (Investment function)G = 30 (government purchases) i) Derive equations fro IS and LM curvesii) Determine the rand y pair at which the two markets are clearing iii) Compute the values of C, I and L.

Consumption and the real interest rate: According to the life-cycle / permanent-income hypothesis, consumption depends on the present discounted value of income. An increase in the real interest rate will make future income worth less, thereby reducing the present discounted value and reducing consumption. To incorporate this channel into the model, suppose the consumption equation is given by Assume the remainder of the model is unchanged from the original setup, as in Table 11.1. (a) Derive the IS curve for this new specification. (b) How and why does it differ from the original IS curve?  

Suppose that a consumer/investor has an initial endowment only for the current period, which is Eo =450. She may consume today or in the next period only (two-period model). The interest rate for borrowing and lending in the capital market is 5% (a)Depict the budget constraint for the investor in an inter-temporal consumption diagram! What is the maximum amount the consumer is able to consume in the next period? (b)The consumption preferences of the consumer/investor are best described by a square root function, defined over current and future consumption. What is his optimal consumption plan? Show your calculations! Depict the results in appropriate diagram. Which amount is invested in the capital market?

a) consider the following IS–LM model: C = c1(Y - T) I = b1Y - b2i M/P = d1Y - d2i Solve for equilibrium output. Assume c1 + b1 < 1.  b) Solve for the equilibrium interest rate. (Hint: Use the LM relation.) c) Solve for investment.

3. Analytic Question on Durable Consumption It is known that durable consumption is more sensitive to interest rates and expected income. In this question, we investigate if this is the case in the context of the model we have been studying. We investigate the following decision: U (c1, c2) 1 max {c1,c2} 2 VCi + xo + subject to the following budget constraints: The time 1 budget constraint: a = Y1 - Ci and the time 2 budget constraint: C2 = Y2 + (1 +r) a. The novelty is that ro is now a variable to represents past purchases of goods 1. You can think of this as a car. In turn, we have that x1 = c1 so a1 is consumption derived utility in period 2 derived from past purchases. For this question assume that B (1+ r) = 1. Answer the following questions. а. Substitute out a from both budget constraints, the one at time 1 and time 2, to write a single intertemporal budget constraint. b. Show that the Euler equation (the equation that relates the marginal utility of consumption to the interest…

Labor Market Y = α (5N – 0.0025N2), where α = 2; N = labor The supply of labor, NS isNS = 55 + 10(1-t)w where t- tax rate = 0.5, w = real wage rate Good Market The desired consumption, Cd is Cd = 300 + 0.8(Y – T) – 200rWhere Y = income, T = taxes, r = real interest rate T= 20 + 0.5YG= 50Desired investment, Id:Id = 258.5 – 250r Money Market Demand for money, Md/P: Md/P = 0.5Y – 250(r + πe), where πe = 0.02 (expected inflation) Money supply = Ms = 9150 a)Find the equilibrium w, Y and N.b)Find the IS-curve and the equilibrium r, C and I.c)Find the LM-curve and the equilibrium P.d)If G increased to 72.5, find the equilibrium w, P, N, r, C and I.e)Discuss the differences between the equilibrium values in d) with a), b) and c). What is your conclusion with regard to the effectiveness of fiscal policy in this model?

5. Using the accelerator model in which the level of inventories in current period depends on the expected sales following this equation: Nt= a ESt Where N stands for the current level of inventories, ESt stands for the level of expected sales and alpha is a parameter equal to 0.6. The growth or increase in inventories is given by AN, = B(N₁-N₁-1), where Beta parameter is equal to 0.3 a) Suppose that the initial level of inventories is zero and the forecasting for sales for this period is equal to 200. Can you quantify the level of inventory investment? What would it be total production in period 1? b) Now suppose that in the second period there growth of inventories is 12%. What is the value of inventory investment for period 2 and forecasting sales for period 2?

Consider the basic Macroeconomic model involving:        Private sector consumption: C = co+c1(Y-T); Y = GDP, T = Taxes        Tax function: T = to+t1Y        Business sector investment: I = io+i2r, r=interest rate        Government spending: G = Go        Exports: X = xo+x1x; x = Exchange rate of the dollar        Imports: M = mo+m1Y+m2x; x = Exchange rate (a) Identify and explain the parameters: co, t1, i2, and m2. (b) Solve this model for the equilibrium GDP (Y*).