Explicit Consumption Functions with Borrowing Constraints: a Continuous Time Approach
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917062523224064 |
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| author | Roulleau-Pasdeloup, Jordan |
| author_facet | Roulleau-Pasdeloup, Jordan |
| contents | There is no known explicit global closed form solution for the standard income fluctuation problem with a borrowing constraint and where wealth accumulates with a constant interest rate $r$. Using a continuous time formulation, I derive an explicit global closed form solution for the case $r=0$ using the Lambert W function. For the case $r>0$, I derive an explicit global closed form approximation that is valid for $r\sim 0$. I then use these to derive explicit expressions for the marginal propensity to consume out of assets and permanent income. I show that the cross-derivative between the two is strictly positive: the consumption consumption is supermodular. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_03452 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Explicit Consumption Functions with Borrowing Constraints: a Continuous Time Approach Roulleau-Pasdeloup, Jordan Theoretical Economics There is no known explicit global closed form solution for the standard income fluctuation problem with a borrowing constraint and where wealth accumulates with a constant interest rate $r$. Using a continuous time formulation, I derive an explicit global closed form solution for the case $r=0$ using the Lambert W function. For the case $r>0$, I derive an explicit global closed form approximation that is valid for $r\sim 0$. I then use these to derive explicit expressions for the marginal propensity to consume out of assets and permanent income. I show that the cross-derivative between the two is strictly positive: the consumption consumption is supermodular. |
| title | Explicit Consumption Functions with Borrowing Constraints: a Continuous Time Approach |
| topic | Theoretical Economics |
| url | https://arxiv.org/abs/2511.03452 |