There are a range of property rights regimes that are possible in agriculture. These range from a landowner who pays fixed wages to her farm worker and keeps all profits from working the land, all the way to a tenant who pays a fixed rental fee to the landowner and keeps all profits from working the land. Somewhere in the middle is a sharecropping arrangement where the landowner and tenant share the revenues from selling their crops (normally in equal proportion). Suppose the agricultural output of a plot of land depends on the inputs y of a landowner and the inputs x of a tenant. Output is given by Q = A[logx + logy] , where A = 10. The price received for the goods is p = 1, the cost of a unit of effort to the tenant is w = 1 and the cost to the landowner of a unit of her inputs is r = 2.
Question:Suppose the landowner and the tenant share output in equal proportions. What will be the levels of x and y? What is total output?
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