MBFM III - Week 10 Tutorial Questions
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MBFM III - Week 10 Tutorial Questions
The objective of this problem is to see what the baseline model and its capital aug-mented counterpart have to say about aggregate supply and demand.
1 Problem #1
Take the baseline model that we examined in class with constant money supply. The individual’s problem in the model results in the optimality conditions
1. Substitute the two period budget constraints into the optimal intertemporal con- sumption trade-o↵ condition. This implies a money demand function. Take the total di↵erential of this equation and construct an expression for the derivative 
. What is required for < 0?
2. Construct the goods market clearing condition for this economy’s equilibrium. From this, identify an Aggregate Demand equation and an Aggregate Supply equa- tion.
3. Assume that < 0. How does Aggregate Demand change with changes in πt+1? How does Aggregate Demand change with variation in πt?
4. How does Aggregate Supply change with changes in πt+1? How does Aggregate Supply change with variation in πt?
5. What would these curves look like if plotted in (Y,πt+1) and (Y,πt) space, respec- tively?
2 Problem #2
Take the baseline model that we examined in class with constant money supply aug- mented by capital savings. For simplicity, assume that capital fully depreciates after production. The individual’s problem in the model results in the optimality conditions
where we assume u\ (c) > 0, u\\ (c) < 0, f\ (k) > 0, and f\\ (k) < 0.
1. Using equality in expected asset returns, take a total differential and show that 
2. Substitute the two period budget constraints into the optimal intertemporal con- sumption trade-o↵ condition through money savings. As in the first question, this implies a money demand function. Using the expression for 
, take the total di↵erential of this equation and construct an expression for the derivative . What is required for < 0?
3. Construct the goods market clearing condition for this economy’s equilibrium. From this, identify an Aggregate Demand equation and an Aggregate Supply equa- tion.
4. How does Aggregate Demand change with changes in πt+1? How does Aggregate Demand change with variation in πt?
5. How does Aggregate Supply change with changes in πt+1? How does Aggregate Supply change with variation in πt?
6. What would these curves look like if plotted in (Y,πt+1) and (Y,πt) space, respec- tively?
2023-06-27