30E00300 Productivity and Efficiency Analysis

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  1. This year the course was organized as a self study course. On previous years there were lectures, assignments and a project as an alternative to the exam. This year there were only some selected slides + selected chapters from the course book (the course book can be gotten as an electronic version from the library). I don’t know how the course will be organized in the coming years, anyone’s guess. For me this self study thing worked out very well since I wouldn’t have had time to go to the lectures anyway. The exam had the following questions this year, again I don’t know what the course will be like in the future:

    Exam 23.5.2016:

    1) A company produces products A and B. Product A requires 2 units of labor and product B requires 4. A total of 160 units of labor can be utilized.

    a) Graph the production possibilities of the combined quantities of A and B that the firm can produce and shade the area of all possible production combinations the firm can produce (including the ones where all resources are not utilized). What is the equation for the production frontier? (5 points)

    b) The company also uses 4 units of machinery time to produce product A and 2 units of machinery time to produce product B. In total the company can utilize 180 units of machinery time. Shade in (to the same graph as in a)) the production possibilities constrained by the machinery time, assuming labor does not restrict output. What is the equation for this production curve. (5 points)

    c) Shade in (to the same graph as in a) and b)) the possible production quantities assuming both labor and machinery restrictions apply and identify the point where the company is most efficient. (5 points)

    d) If you did not have the graph in part c), what equations would you use to determine the most efficient point? (5 points)

    e) If the company wanted to maximize the amount of product A it produces, which one of the inputs (labor or machinery time) will not be totally utilized? (5 points)
    2) Figure 3.6 from the book is given (graph of Technical and Allocative Efficienies). Explain and calculate the technical efficiency (TE), cost efficiency (CE) and allocative efficiency (AE). (10 points)
    3) The production function of a company is Q=15*(K^0.2)*(L^0.8). The price per unit of labor is €100 and the price per unit of capital is €200.

    a) What are the returns to scale for the company? (5 points)
    b) Calculate the conditional input demands for labor and capital. (10 points)
    c) What is the cost function in terms of prices and level of output? (10 points)
    d) What is the marginal rate of technical substitution of labor for capital? (10 points)
    4) For the given set representation Ψ(x) {(x,q) | q: x can produce q}.
    a) What is meant by disposability and under what conditions does it apply? (10 points)
    b) Explain what is the radially expanded distance function associated with the input vector and how it is formed for the set. (10 points)
    5) Explain what is scale efficiency and how it is calculated. (10 points)


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