10. The very small economy of Lilliput has a total labor force of 20 workers. These workers can produce two goods, manufactures and food. In production of manufactures, the marginal product of labor depends on employment as follows: Number of Workers Elm-mu m---mnn-n In the food sector, the marginal product of labor is independent of employment, and is 5. The world price of a unit of food is $10, and the world price of a unit of manufactures is $10. Show all work and explain how you obtain your answers. a. Suppose there were no distortion in the labor market; find (i) the wage rate, (ii) the allocation of labor between manufactures and food, (iii) the output of each good, and (iv) the total dollar value of output in this economy. b. Now, suppose that for some reason the minimum wage in the manufactures sector is $100. Full employment, however, is maintained. Find (i) the allocation of labor between manufactures and food, (ii) the output of each good, and (iii) the total dollar value of output in this economy. (iv) How large is the cost of the distortion in terms of the dollar value of lost output? c. Finally, suppose that workers migrate from the country to the city until the wage of city workers multiplied by the probability of being employed equals the rural wage. Find (i) the urban unemployment rate, (ii) the allocation of labor between manufacturing, urban unemployment, and the food sector, (iii) the output of each good, and (iv) the total dollar value of output in this economy. (v) How large is the cost of the distortion in terms of the dollar value of lost output, when compared to part a