Consider land as an additional productive factor and assume that the production function is: YIAX'IL1_\

Consider land as an additional productive factor and assume that the production function is: Y A xaL1a where 0 < a < 1, and X is a factor composed of the factors land (D) and capital (K), such that: X D KI- Capital can be produced while the land factor cannot be increased, i.e., it remains in time. Let s, n and be positive constants. (a) Express the production function per worker in terms of land per worker (d) and capital per worker (k). b) Write the equation for the increase in capital per worker (k). (c) Show that this model implies that the level of output per worker tends to zero over time. Why does this result obtain? (d) Suggest some modification in the production function that maintains the productive factor land but prevents the result in (c) from being obtained, showing that result.