Derive an expression for the firms marginal rate

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Reference no: EM132489005

Problem 1

A firm has the production function Q = LK + 2K. The associated marginal products are,

MP_L = K and MP_K = L + 2.

The wage is w = $200, and the rental price of capital is r = $800.

Required:

(a) Are the marginal products of labour and capital diminishing? Briefly explain.

(b) Derive an expression for the firm's marginal rate of technical substitution. Is the marginal rate of technical substitution diminishing? Briefly explain.

(d) What is the cost to the firm of producing Q = 256 units?

Problem 2
Three (3) identical firms produce widgets. Each firm faces a constant marginal cost of $10 per widget, and has fixed costs of $15,000. The firms compete by selecting quantities (Cournot Competition). Inverse demand in the market is given by the equation,

P = 50 - Q/100

where P represents the market price and Q is the total quantity produced by the three firms.

Required:
(a) Derive the total cost function for the typical firm. (Hint: Use QA to represent the quantity produced by this firm.)

(b) Derive the profit function for the typical firm. (Hint: Use X to represent the com¬bined production of the remaining two firms.)

(d) Find the equilibrium quantity of the typical firm.

(e) Find the equilibrium market price and the profits of the typical firm.

(f) Explain how would you expect the structure of this market to change over time. Maximum length 100 words. (Hint: You do not need to do any further calculations for this part of the Problem.)

Reference no: EM132489005

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