intro to farmHH

notebooks/FarmHousehold.ipynb

@@ -7,6 +7,25 @@
     "# Farm Household Models"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Most economics textbooks typically analyze the decisions of firms separately from the decisions of households.  In this artificial but useful dichotomy the firm organizes production and hires factors of production while households own the factors of production (and ownership shares in firms) supply these factors on the market. \n",
+    "\n",
+    "However many households in developing countries -- and not just rural households -- operate a small farm, garden plot, store or other type of business (or they might have to fall back on that option at certain times) at the same time that they possibly also sell or hire labor in the labor market.  Indeed a large literature suggests that one defining characteristic of developing countries is the large fraction of its labor force who are self-employed 'own account' workers and/or who run small businesses alongside wage labor jobs (e.g. Gollin, 2008).  \n",
+    "\n",
+    "Given the importance of the topic it's useful to build models that start by thinking of households as potential producers and/or market participants.  Here we offer stylized representations of the so called 'farm household model' or 'agricultural household model' (Singh, Squire, Strauss, 1986).\n",
+    "\n",
+    "In these models the household acts both as a consumption unit, maximizing utility over consumption and 'leisure' choices and as a production unit, deciding how to allocate factors of production to the household farm or business. \n",
+    "\n",
+    "A key question in this literature is whether the household's production decisions (such as its choice of labor and other inputs and the scale of production) are *separable* or not from its preferences and endowments (e.g. consumer preferences, household demographic composition and ownership of land and other resources). For example, will a rural farm household with more working age adults run a larger farm compared to a neighboring household that is otherwise similar and has access to the same technology but has fewer working-age adults?  If the households decisions are non-separable then the answer might be yes: the larger household uses of its larger labor force to run a larger farm.    \n",
+    "\n",
+    "When households are embedded in well functioning competitive markets however we tend to expect the household's decisions to become separable: acting as a profit-maximizing firm it first optimally chooses labor and other input allocations to extract maximum profit income from the farm and then makes optimal choices over consumption and leisure subject to its income budget which includes those maximized profits and income from selling its labor endowment.  In the simple example above of two otherwise identical households the separable farm household model would predict that both households run farms of similar size and use wage labor markets to equalize land-labor ratios and hence marginal products of labor across farms.  The larger household would be a net seller of labor on the market compared to the smaller household. \n",
+    "\n",
+    "Another way to state the separation hypothesis is that if they have access to markets the marginal production decisions of farms (and firms more generally) should not depend on their owners' ownership of tradable factors (except in so far as it might raise their overal income) or their preferences in consumption. When markets are complete then production decisions will be separable, the price mechanism will equalize the marginal products of factors across uses, and the initial distribution of tradable factors should not matter for allocative efficiency (the first and second welfare theorems).  Much of modern micro-development since at least the mid 1960s however is concerned with how transactions costs, asymmetric information, conflict and costly enforcement can lead to market frictions and imperfections that make production decisions non-separable, which then means that the initial distribution of property rights (over land and other tradable factors) may in fact well matter for determining the patterns of production organization and its efficiency in general equilibrium. A good example of such analysis is Eswaran and Kotwal (1986) paper on \"Access to Capital and Agrarian production organization,\" which explores how the combination of transaction costs in labor hiring and in access to capital can lead to a theory of endogenous class structure or occupational choice which can change dramatically depending on the initial distribution of property rights. "
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -18,7 +37,16 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "A self-sufficient farm household $i$ with land and labor endowment $(\\bar T_i, \\bar L_i )$ is completely cut off from product and factor markets.  It allocates labor maximizes utility over consumption and leisure"
+    "We'll start with a non-separable model, inspired by the work of the Russian agronomist Alexander Chayanov whose early 20th century ideas and writings on \"the peasant economy\" became widely influential in anthropology, economics, and other fields.  Chayanov played a role in the Soviet agrarian reforms but his focus on the importance of the household economy led him to be (presciently) skeptical of the appropriateness and efficiency of large-scale Soviet farms. He was arrested, sent to a labor camp and later executed.  \n",
+    "\n",
+    "The following model is not anywhere as rich as Chayanov's description of the peasant household economy but instead a stripped down version close in spirit to Amartya Sen's (1966) adaptation. "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Farm household $i$ has land and labor endowment $(\\bar T_i, \\bar L_i )$.  We can assume that it can buy and sell the agricultural product at a market price $p$ but in practice we will model the household as self-sufficient and cut off from the market for land and labor.  The household (which we treat as a single decision-making unit for now) allocates labor maximizes utility over consumption and leisure"
    ]
   },
   {
@@ -32,7 +60,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "subject to the constraints that consumption $c_i$ not exceed output and the sum of hours in production $L_i$ plus hours in leisure $l_i$ not exceed the household's labor endowment $\\bar L_i$"
+    "Although we haven't included it above, we think of the utility function $U(c_i,l_i;A)$ as depending on 'preference shifters' $A$ which might include such things as the household's demographic composition or things that affect it's preference for leisure over consumption). \n",
+    "\n",
+    "The household maximizes this utility subject to the constraints that consumption $c_i$ not exceed output and that the sum of hours in production $L_i$ plus hours in leisure $l_i$ not exceed the household's labor endowment $\\bar L_i$"
    ]
   },
   {
@@ -47,7 +77,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Substituting the constraints into the objective reduces the problem to one of choosing the right allocation of labor to production:"
+    "Substituting the constraints into the objective allows one to redefine the problem as one of choosing the right allocation of labor to production:"
    ]
   },
   {
@@ -73,6 +103,13 @@
     "which states that the farm household should allocated labor to farm production up to the point where the marginal utility benefit of additional consumption $U_c \\cdot F_L$ equals the opportunity cost of leisure.   "
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Since the household sets the marginal product of labor (or shadow price of labor) equal to the marginal rate of substitution between leisure and consumption $F_L = U_l/U_c$ and the latter is clearly affected by 'preference shifters' $A$ and also by the household's land endowment.  The shadow price of labor will hence differ across households that are otherwise similar (say in their access to production technology and farming skill).  For example households with a larger endowment of labor will run larger farms.  "
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -581,6 +618,15 @@
     "Since every farm takes the market wage as given the marginal product of labor will be equalized across farms. The shadow price of labor will equal the market wage on all farms, regardless of their land size. The land labor ratio and hence also the marginal product of land will also equalize across farms so output per unit land will also remain constant."
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Testing for Separation in Household models\n",
+    "\n",
+    "There are basically two"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -608,7 +654,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.4.4"
+   "version": "3.5.1"
   }
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  "nbformat": 4,