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: 0 ( , ) L r Y m kY hr =+− Real money supply: 0
sM z P =
Consumption: 0 () C C c Y T = + −
Learning Objective in this assignment: - Get comfortable with
concepts presented in Section 4 (IS-LM model) - Be able to derive
the IS-LM graphically and algebraically using the standard model
presented in class - Be able to derive new IS-LM relationships with
minor changes to the modeling assumptions - Be able to derive
government spending (or other policy) multiplier with any given
IS-LM model
2
Government spending: G Investment demand: 0 I I 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: ??=?? �+????, where ?? � 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.
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