ECOS2902 Practice Mid Section B PDF

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Practice mid-semester exam short-answer questions 1. Consider an IS-LM model with consumption and investment functions: C = 1 + 0.2 (Y - T), I = 3 + 0.3Y - 20i, and suppose G = 2 and T = 10. Central bank sets an interest rate of ฀฀ = 10%. The real money demand is given by: Md / P = 5Y - 50i. (a) Derive the IS curve. (b) Derive the LM curve. (c) Solve for the equilibrium output, interest rate and real money supply in the short run. Due to a drop in consumer confidence, consumers reduce their consumption level, so that the consumption function now becomes: C = 0.2 (Y - T), (d) Compute the new equilibrium output, interest rate and real money supply in the short run. (e) Compute the old and new equilibrium investment levels. How does the drop in consumer confidence affect the equilibrium investment level? Explain the intuition behind this change. To give a quick boost to the economy and bring the equilibrium output back to the original level identified in part (c), the central bank decides to launch an expansionary monetary policy by reducing the interest rate. (f) Solve for the required interest rate that can achieve such a recovery. To achieve this interest rate, what is the required real money supply? (g) Draw an IS-LM diagram to represent the drop in consumer confidence and the expansionary monetary policy response. Label all axes and curves and mark all the values and equilibrium points appropriately.

2. Suppose the economy is described by the following behavioural equations. Assume the central bank controls the interest rate. C = c0 + c1(Y –T) I = b0 + b1Y – b2i Md / P = kY – hi G = G0 T = T0 i = i0

Consumption Investment Money demand Exogenous government purchases Exogenous taxes Interest rate

(a) Derive the IS curve. (b) Derive the LM curve. (c) Solve for the equilibrium output in the short run. (d) Solve for the equilibrium real money supply. Now suppose

c0 =200 c1 = 0.25 b0 = 150 b1 =0.25 b2 =1000 k= 2 h=8000 G0=250 T0=200 i0=0.05

(e) Solve for the equilibrium values of C, I, Y, and real money supply. Verify the value you obtained for Y by adding up C, I and G. (f) Now suppose that government spending increases to G=400. Solve for the new equilibrium values of C, I, Y, and real money supply. (g) Now suppose that in response to the fiscal expansion, the central bank increases the interest rate to 20%. Solve for the new equilibrium values of C, I, Y, and real money supply.

3. Suppose workers can be either employed or unemployed. The job separation rate is a constant s = 0.03 per month. Each month, a number m of unemployed workers are matched to new jobs m = fu where f is the job finding rate for unemployed workers. Equivalently, m vacant job positions are filled m = qv where q is the job filling rate for firms. To determine the job finding rate f and job filling rate q we assume the number of matches is given by the Cobb-Douglas matching function m = F(u, v) = √uv (a) Provide formulas for the job finding rate f and job filling rate q in terms of the labour market tightness ratio θ = v/u. Is the job finding rate increasing or decreasing in labour market tightness? Explain. (b) Suppose the value to a firm of a filled job is J = 2 and the cost of posting a vacancy is c = 4. Calculate the equilibrium labour market tightness ratio θ ∗. Using this value for θ∗ , solve for the steady-state job finding rate and steady-state unemployment rate. (c) Suppose the economy goes into recession and the value of a filled job falls to J = 1. Calculate the new equilibrium values of labour market tightness and unemployment. Give intuition for all your answers. (d) Returning to the case of J = 2, suppose the matching function is instead m = 0.5√uv Is the labour market more or less efficient with this matching function? Calculate the new equilibrium values of labor market tightness and unemployment with this matching function. How do these values compare to your answers from part (c)? Explain.

4. Suppose the change in unemployment ฀฀฀฀ is given by ฀฀฀฀+1 − ฀฀฀ ฀ = ฀฀(1 − ฀฀฀฀ ) − ฀฀(฀฀฀฀ )฀฀฀฀ with constant job separation rate s per month and with monthly job finding rate given by ฀฀ ,฀฀0 < ฀฀฀ ฀ < 1 ฀฀(฀฀฀฀ ) = ฀฀฀฀

with constant match efficiency M and labour market tightness where ฀฀฀ ฀ = ฀฀฀฀ /฀฀฀฀ where ฀฀฀฀ is the job vacancy rate. Firms post vacancies until the vacancy-filling rate ฀฀(฀฀฀฀ ) satisfies ฀฀(฀฀฀฀ )฀ ฀ = ฀฀ where J is the value of a filled position and where c is the cost of creating a vacancy. (a) Let ฀ ฀ = 0.5, s = 0.053, M = 1, J = 1 and c = 1. Solve for the equilibrium labour market tightness ฀฀ ∗, steady-state job finding rate, steady-state unemployment rate, and steady-state vacancy rate. (b) Suppose the economy goes into a recession and the value of a filled job J falls by 10%, i.e., to J = 0.9. Calculate the new equilibrium values of labour market tightness, the job finding rate, the unemployment rate, and vacancy rate. How do these values compare with those you found in part (a)? Give intuition for your answers. (c) Suppose instead that matching efficiency M falls by 10%, i.e., to M = 0.9. Calculate the new equilibrium values of labour market tightness, the job finding rate, the unemployment rate, and vacancy rate. Does a 10% fall in M affect these variables just the same as a 10% fall in J? Why or why not? Give intuition for your answers. (d) Now suppose instead that the separation rate s rises by 10%, i.e., to s = 0.0583. Calculate the new equilibrium values of labour market tightness, the job finding rate, the unemployment rate, and vacancy rate. Does a 10% rise in s affect these variables just the same as a 10% fall in M? Why or why not? Give intuition for your answers. (e) Now suppose that ฀ ฀ = 0. Does a 10% fall in M have bigger or smaller effects on unemployment and labour market tightness than in part (c)? Explain....