Exercise 9.1

The Demand Schedule Of Nontradables

⬅ Return

Problem

In section 9.1, we assume that the aggregator function, \(A(c^T,c^N)\), given in (9.2), is increasing, concave, and linearly homogeneous.

1. Show that these assumptions are sufficient to ensure that the demand schedule of nontradables, given in equation (9.5) and depicted in figure 9.2, is downward sloping in the space \((c^N,p)\), holding constant \(c^T\).

2. Show that the aforementioned assumptions about the aggregator \(A(c^T,c^N)\) are sufficient to guarantee that increases (decreases) in \(c^T\) shift the demand schedule up and to the right (down and to the left).

3. Assume that the aggregator function takes the Cobb-Douglas form \(A(c^T,c^N) =\sqrt{c^T c^N}\). Find the demand function of nontradables.

4. Now assume the CES form \(A(c^T,c^N) = \left[a (c^T)^{1-\frac{1}{\xi}} + (1-a) (c^N)^{1-\frac{1}{\xi}}\right]^{\frac1{1-\frac1{\xi}}}\). Derive the demand function of nontradables. Interpret the parameter \(\xi\).

Answer

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