ECON 30001 Assignment, University of Melbourne, Semester 02, 2025. YA = LαAK 1−α A , YM = L β MK 1 Consider a small open economy with two sectors, Agriculture (A) and Manufacturing (M). Produc- tion in each sector uses capital (K) and labor (L This assignment is due on 5pm on 17October, 2025. Students can register their group under “People” on Canvas under the “Assignment 1 Group tab” for this subject. A maximum of 2 students are

allowed in a group and members may come from different tutorials. Those who have not registered

their groups can submit an individual assignment. Students who choose to work individually do not

need to register. Submit the assignment by uploading a file via the Assignments tab of Canvas. Only

one group member needs to submit the assignment. Please make sure that the names and student

numbers, and tutors of all group members are clearly stated on the assignment. Please note that the

University and the teaching staff take academic integrity seriously. Please be aware that plagiarism

is unacceptable. Further details can be found in the subject guide. ) under Cobb–Douglas technologies: −β M , with α > β, so that Agriculture is relatively labor-intensive. Firms in each sector are competitive and maximize profits: πj = PjYj −WLj − RKj, j ∈ {A, M}, where Pj is the good’s price, W the common wage, and R the rental rate of capital. The economy has fixed endowments of labor and capital: L¯ and K¯. 1. Part (a) Derive the first-order conditions for labor and capital demand in each sector. Use these to obtain an expression of relative demand for labor as a function of their relative factor prices. Plot the relation- ship between relative demand and relative factor prices with L/K on horizontal axis and W/R in vertical axis. 2. Part (b) Using the factor market clearing conditions: L¯ = LA + LM, K¯ = KA + KM Derive an expression for the economy-wide capital-labor ratio K¯L¯ as a function of the factor price ratio W R and the sectoral labor allocations. Define λ = LA L¯ as agriculture’s share of total labor. Express your final answer in terms of λ, α, β, and WR . 1 3. Part (c) Your expression for λ in Part (b) shows that the labor allocation depends on both the factor en- dowment ratio K¯L¯ and the equilibrium factor price ratio W R . Explain what determines W R in general equilibrium. Hint: In lectures we use θ as the share of capital in sector A. 4. Part (d) Now instead, do a cost minimization for the producer to obtain unit costs for both sectors. Use these

conditions to obtain conditional factor demands for both sectors. Use this to obtain the relationship

between relative price of goods and relative price of factors. ) 2 51作业君版权所有