land - Notes on the Economics of Land Use Susan E Stratton...

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Notes on the Economics of Land Use Susan E. Stratton 1 Land Rent The key concept for land rent is tied to scarcity. Since land is scarce, the owner of the land can claim the economic value of that scarce resource. In our basic model, land is the only scarce resource, so only land can earn positive economic profits. In some of our models all land is identical. In others, land varies by location or productivity. Land values or rents will adjust to consider those changes in either land or productivity. The models we develop are designed to show us how they adjust. 1.1 Approach 1: Marginal and average worker productivity Consider a landowner who can hire workers at a wage rate w . As more workers are added, their marginal and average productivity will (eventually) decline. The landowner will max- imize profits by solving max n pq ( n ) - wn (1) where n is the number of workers, p is the price of output and q ( · ) gives productivity as a function of the number of workers. Clearly, the solution to this problem is pq ( n ) - w = 0 (2) or that marginal productivity is equal to the wage rate. Because we’ve assumed an infinite supply of workers at a wage rate of w , the workers will all receive w . The landowner will get pq ( n ) - wn or n pq ( n ) n - w . This is equivalent to the average product per worker minus the wage rate times the number of workers. We can draw two different graphs showing this. 1
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1.2 Approach 2: Variation in land productivity Consider multiple plots of land. Plot A is very productive, plot B less so, and so on. Mathematically, this means that MP A > MP B > MP C and so on. 1.2.1 Fixed supply of workers, two plots We’ll equate the marginal product of labor on the two plots and set the wage rate that way. Clearly, if the marginal product of labor where higher on one plot than the other, we should shift workers toward the more productive plot. Thus the marginal product must be equal in equilibrium. 1.2.2 Infinite elastic supply of workers All landowners solve a problem like the one in section 1.1, setting the marginal productivity of their land equal to the wage rate. Each plot earns a rent determined by its marginal productivity. The marginal plot of land earns zero economic rent. 2
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1.2.3 Upward-sloping labor supply curve In this case, the wage rate is determined by the intersection of the marginal product on the marginal plot with the labor supply curve. How is surplus divided?
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