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Economics

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2. (i) The production function for a firm is given by
Q = LK
where Q denotes output; Land K labor and capital inputs.
Wage rate and rental rate are given by w and r respectively.
(a) Show whether or not the above production function exhibits
diminishing marginal productivity of labor.

(b) Determine the nature of the Return to Scale as exhibited by the above
production function

(c) Using the Lagrangean Multiplier method, calculate the least cost
combinations of labor and capital and the resulting long run total cost
function for the above production function. Explain the economic
significance of the Lagrangean Multiplier and calculate its value.

3(d) Using the above cost function, calculate the numerical value of long run
total cost when Q =225, w = 16 and r = 144.

(e) Using Excel- Solver verify your answer to (d) above.

(ii) As the manager of an 80-unit motel you know that all units are occupied
when you charge $60 a day per unit. Each occupied room costs $4 for
service and maintenance a day. You have also observed that for every x
dollars increase in the daily rate above $60, there are x units vacant.
Determine the daily price that you should charge in order to maximize
profit.

  • Economics -

    I can not help with the first part, do not have formulas or understand notation.
    ii. ) fully occupied profit = 80*60 -80*4 = 4480
    price/unit = 60 + x
    no of units occupied = 80 - x
    cost = 4 (80-x)
    so profit = (80-x)(60+x) - 4(80-x) = P
    P = (80-x)(56+x)
    P = 4480 + 24 x - x^2
    max where dP/dx = 0 (or find vertex of parabola)
    2 x = 24
    x = 12
    price = 60 + 12 = 72

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