Consider a country in which there are 2 sectors called Sector 1 and Sector 2. The production functions and the marginal products in the two sectors

Consider a country in which there are 2 sectors called Sector 1 and Sector 2. The production functions and the marginal products in the two sectors are:

Y1=10*(L1)0.5 and MPL1=5/(L1)0.5Y2=20*(L2)0.5 and MPL2=10/(L2)0.5

where L1 is the number of workers employed in Sector 1 and L2 is the number of workers employed in Sector 2. The prices of goods in both sectors are equal to 1. The total number of workers in the economy is 2,000. The only difference between the sectors is that in Sector 1 workers are paid their average products, whereas in Sector 2 they are paid their marginal products. Workers move freely between sectors so that the wages are equal.

1. (a) Draw a diagram for this economy. (See Figures 10. 3 – 10.5 for the idea).
2. (b) Calculate how many workers will work in each sector.
3. (c) Assume that now producers in both sectors behave optimally. Draw a diagram for this economy. (See Figures 10. 3 – 10.5 for the idea).
4. (d) Calculate the optimal number of workers in each sector.

(e) Use your answers from (b) and (d) to answer the following question: compared to the optimal allocation of workers, what sector has too many workers, and what sector has too small employment?

(f) Assume that in both sectors producers still behave optimally and that the government introduces the minimum wage of 1. Draw a diagram for this situation. What will it do to the employment in each sector? Is this policy efficient? (Hint. Before drawing the figure calculate the optimal wage and compare it with the minimum wage).

(g) Finally, assume that after the introduction of the minimum wage of 1, the productivity in Sector 1 has risen so that now Y1=100*(L1)0.5 and MPL1=50/(L1)0.5. How will this change your answer to part (f)? (Hint: calculate the new optimal wage and compare it with the minimum one).

Home Assignment #7: Due on Wednesday, March 31st, 5 pm (Toronto time)
Show all your calculations and explain all your answers
1. (100 points). Consider a country in which there are 2 sectors called Sector 1 and Sector 2. The
production functions and the marginal products in the two sectors are:
Y1=10*(L1)0.5 and MPL1=5/(L1)0.5
Y2=20*(L2)0.5 and MPL2=10/(L2)0.5
where L1 is the number of workers employed in Sector 1 and L2 is the number of workers employed
in Sector 2. The prices of goods in both sectors are equal to 1. The total number of workers in the
economy is 2,000. The only difference between the sectors is that in Sector 1 workers are paid their
average products, whereas in Sector 2 they are paid their marginal products. Workers move freely
between sectors so that the wages are equal.
(a) Draw a diagram for this economy. (See Figures 10. 3 – 10.5 for the idea).
(b) Calculate how many workers will work in each sector.
(c) Assume that now producers in both sectors behave optimally. Draw a diagram for this economy.
(See Figures 10. 3 – 10.5 for the idea).
(d) Calculate the optimal number of workers in each sector.
(e) Use your answers from (b) and (d) to answer the following question: compared to the optimal
allocation of workers, what sector has too many workers, and what sector has too small employment?
(f) Assume that in both sectors producers still behave optimally and that the government introduces
the minimum wage of 1. Draw a diagram for this situation. What will it do to the employment in each
sector? Is this policy efficient? (Hint. Before drawing the figure calculate the optimal wage and
compare it with the minimum wage).
(g) Finally, assume that after the introduction of the minimum wage of 1, the productivity in Sector
1 has risen so that now Y1=100*(L1)0.5 and MPL1=50/(L1)0.5. How will this change your answer to
part (f)? (Hint: calculate the new optimal wage and compare it with the minimum one).