Question

The information below describes the current state of the economy for the Kingdom of Westeros. All coefficients (e.g. m0) represent positive constants, and c is bounded between 0 and 1. T is lump sum tax. Assume prices are fixed in the short run.

Real money demand: L(r,Y) = m₀ + kY - hr

Real money supply: M_s/P = z₀
Consumption: C = C₀ +c(Y-T)

Government spending: G

Investment demand: I = I₀ - br

a. Derive an expression for the LM curve for Westeros. What is the slope of the LM curve? Is it positive or negative (explain why)?
b. Derive an expression for the IS curve for Westeros. What is the slope of the IS curve? Is it positive or negative (explain why)?
c. Derive the government spending multiplier using the IS-LM model (i.e. you need to solve for equilibrium Y before calculating the multiplier). Comment on the sign and size of the multiplier.
d. Suppose that Queen Cersei of Westeros decided to enact a new tax system where tax is no longer just a lump sum but is dependent on income: ?= Ť tY, where Ť is some fixed amount and t is the marginal tax rate bounded between 0 and 1 (if income rises by $1, taxes rise by t × $1). Re-derive an expression for the IS curve for Westeros under this new tax code. What is the slope of the IS curve now? Is it positive or negative (explain why)? Is the curve steeper or flatter than the case in part a (explain why)?
e. Derive the government spending multiplier using the new IS curve in part d above (don’t forget to solve for the equilibrium Y first using the new IS curve before calculating the multiplier) and compare the government spending multiplier here with what you derived in part c. Which multiplier is bigger (explain why)?
f. Graphically illustrate the two multipliers with an increase in G and discuss how this tax code change affects the effectiveness of fiscal policy expansions using government spending.

Answer 1