Macroeconomic questions

EC214 Macroeconomics Assignment: Set Exercise

Christos Mavrodimitrakis∗

November 2025

1 Instructions

The Analytical Exercise, below, is based on Lectures 1-6 and Problem Sets 1-5. It covers the first part of our module on Business Cycles; namely, the IS-(LM)-PC-MR model. Please read each question ((i) to (xvi)) carefully. The marks for each question are noted; and they sum up to 100. You should answer all questions. The deadline to submit is Wednesday, December 10, 2025, at noon (12pm). You submit via Turnitin. The Submission point can be found in your module’s Blackboard page; in the Assessment Section → Assessment - Set Exercise. Your answers should be written in Word; and any algebra derivations or graphs should be uploaded as photos. Please make sure to provide clear explanations; and step by step derivations. Everything should be your own work. Please do not upload pictures from the module’s Learning Material.

2 Analytical Exercise

Consider the following behavioural equations that describe the goods market in a closed economy:

C = c0 + c1y disp − c2r

T = ty

I = a0 − a1(r + x)

where C is consumption, ydisp = y−T is disposable income, y is income, T is taxes (net of transfers), I is investment, r is the real policy rate and x > 0 defines a risk premium; and c0, a0, a1, c2 > 0 and c1, t ∈ (0, 1). Also, assume that government spending, G, is exogenous.

(i) Thinking of the life-cycle theory of consumption, provide an interpretation of the consumption function, above. In particular, what can be captured by the autonomous part of consumption, c0? Why consumption is negatively affected by the real policy rate?

(5 marks)

(ii) Derive and interpret the IS relation. What is the value of the multiplier for a change in autonomous spending, and what is the value of the slope of the IS relation?

(6 marks)

(iii) How does this IS relation differ from the one that can be obtained under the standard Keynesian consumption function? In that, setting c2 = 0? I.e., which are the implications of forward-looking behaviour (the life-cycle theory) on the IS relation? If there are more households in the economy that follow the permanent income hypothesis, what does this imply for the marginal propensity to consume, c1; hence for the IS curve?

(5 marks)

(iv) Suppose the central bank chooses a real policy rate of r = r̄, when financial markets are in equilibrium (following the liquidity preference theory). Solve for the short-run equilibrium output in this economy, and depict simultaneous equilibrium in the goods and financial markets in a graph.

(5 marks)

∗University of Reading, School of Philosophy, Politics and Economics, Department of Economics, Edith Morley Building, Room 192, Whiteknights Campus, RG6 6UR, Berkshire, UK. Tel: +44 (0)118 378 4671; email: [email protected].

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(v) Let us assume that the demand for real money balances, M P , where M is money and P is the general price level,

is given by:

M

P = d1Y − d2i

where i is the nominal interest rate; and d1, d2 > 0. Solve for the equilibrium level of the supply of real money balances, assuming that πE = 0. Draw the necessary graph that depicts equilibrium in the money market.

(5 marks)

(vi) Provide an interpretation for the tax rule, T = ty. Does this rule imply a counter-cyclical or a pro-cyclical tax policy? Derive the new IS relation, assuming instead that T = t0 + t1Y , where t0 > 0 and t1 = t, like before; as well as the new equilibrium output and real money balances. Comment on your results.

(5 marks)

(vii) Consider now, an increase in government spending that is (partly) financed by an increase in the autonomous part of taxation, t0; specifically, 50% of the change in government spending. Does this imply an expansionary or a contractionary fiscal policy (at equilibrium)? What is the condition for this to define an expansionary fiscal policy? Compute the new short-run equilibrium output and the change in the government’s (primary) budget (at equilibrium).

(8 marks)

(viii) What should the central bank do to keep output constant? Compute the needed change in the real policy rate and depict the new equilibrium in a graph.

(6 marks)

(ix) Compute the change in the real money balances needed in (viii), above. Draw the necessary graph that depicts equilibrium in the money market.

(6 marks)

(x) Assume the following numerical values for the model’s parameters: c0 = 400; c1 = 0.6; G = 500; t0 = 400; a0 = 300; t1 = 0.25; c2 = 200; a1 = 2000; r̄ = 5%; x = 2%; d1 = 0.5; d2 = 200; and in (vii), the new government spending is G

′ = 600. Compute the numerical values for (a) the short-run equilibrium level of output in (iv); (b) the

real money balances in (v); (c) the new equilibrium output and real money balances in (vi); (d) the new short-run equilibrium output and the change in government’s budget constraint in (vii); (e) the needed change in the real policy rate in (viii); (f) the needed change in the real money balances in (ix). Round any numerical value to two decimal points.

(12 marks)

(xi) Consider now the IS-PC-MR model. The IS relation is given by:

yt = A− art−1

where t is the time subscript; and A, a > 0. Define A and a, based on the IS relation you derived above, in (vi). Which are their determinants?

(5 marks)

(xii) Consider now the following Phillips Curve (PC) relation that describes the supply-side of the economy:

πt = πE t + α(yt − ye)

where π is the inflation rate and ye is potential output; and α > 0. Further assuming that πE t = χπT + (1 −

χ)πt−1, where πT is the target rate of inflation and χ ∈ (0, 1) is the central bank’s credibility parameter, provide an interpretation of the PC relation using the theory of conflict inflation.

(5 marks)

(xiii) Assume that the central bank follows the Monetary Rule (MR):

yt − ye = −αβ(πt − πT )

where β > 0 is the central bank’s degree of inflation aversion. Assume that the economy experiences a financial crisis in period 0, in that the risk premia increase; and private sector’s confidence decrease. How can this be captured in our model? In particular, assuming that before the shock the economy is at medium-run equilibrium (in (vi)), explain/prove that ∆y0 = ∆A; and π0 − πT = α∆A. What defines ∆A? Is it positive or negative?

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(6 marks)

(xiv) Compute inflation and output in period 1 as deviations from medium-run equilibrium; and the real policy rate that the central bank should set in period 0 as deviations from the stabilising real policy rate, rS .

(8 marks)

(xv) Explain how the central bank will guide the economy back to medium-run equilibrium, when χ = 0.5; and draw the necessary graph(s). What is the difference with the cases of firmly anchored expectations and adaptive expectations?

(8 marks)

(xvi) Assume now that the zero-lower-bound constraint binds; i.e., the financial crisis is quite severe (like the Great Recession). Does this economy fall into a deflation trap? Does the formation of expectations matter; i.e., whether we consider adaptive or firmly/partially anchored expectations? Now that conventional monetary policy has become ineffective, what other policies can either the central bank or the government implement to guide the economy back to medium-run equilibrium? No algebra or graphs are required.

(5 marks)

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