a. Demonstrate that the production functions satisfy the conditions for monotonically increasing, diminishing return to labor, and constant returns to scale. b. If labor markets are perfectly competitive, in each sector the value of the marginal product of labor will be equal to the wage rate. Write these two conditions. Make sure to base your answer on the provided production functions. c. Combine the two conditions above to get the relationship between the relative price of corn and potatoes, and the allocation of labor to the two sectors (Lc, Lp). If the relative price of corn decreases, what happens to the allocation of labor between the two sectors?

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