1. Suppose that a firm has two machines with different production technologies: 0.60.4 f(r1,r2) = 3T+2/T and g(F1, 12) = . %3D The factor prices are wi = 3 and wa = 2. (a) Derive the cost functions cf and c, for machines f and g, respectively. (b) If the firm can use only one of the machines at a time, which machine will be used? (c) If the firm can run both machines at the same time, how will it organise its production? Derive the firm's cost function c. (Hint: Express the firm's cost as k(m, n) = cr(m) + c, (n) when it is producing q= m+n units, where f is used to produce m units, and g is used to produce n units.) (d) Suppose now that the second technology has a fixed cost of 20, so the cost function C. has an extra 20 in addition to what it used to be. (This fixed cost is incurred

1. Suppose that a firm has two machines with different production technologies: 0.60.4 f(r1,r2) = 3T+2/T and g(F1, 12) = . %3D The factor prices are wi = 3 and wa = 2. (a) Derive the cost functions cf and c, for machines f and g, respectively. (b) If the firm can use only one of the machines at a time, which machine will be used? (c) If the firm can run both machines at the same time, how will it organise its production? Derive the firm's cost function c. (Hint: Express the firm's cost as k(m, n) = cr(m) + c, (n) when it is producing q= m+n units, where f is used to produce m units, and g is used to produce n units.) (d) Suppose now that the second technology has a fixed cost of 20, so the cost function C. has an extra 20 in addition to what it used to be. (This fixed cost is incurred

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

100%

1. Suppose that a firm has two machines with different production technologies:
f(r1, r2) = 3 +22 and g(r1,12) .
The factor prices are wi = 3 and wy = 2.
%3D
(a) Derive the cost functions cf and c, for machines f and g, respectively.
(b) If the firm can use only one of the machines at a time, which machine will be
used?
(c) If the firm can run both machines at the same time, how will it organise its
production? Derive the firm's cost function c. (Hint: Express the firm's cost as
k(m, n) = c(m) +c,(n) when it is producing q = m+n units, where f is used to
produce m units, and g is used to produce n units.)
(d) Suppose now that the second technology has a fixed cost of 20, so the cost function
Cg has an extra 20 in addition to what it used to be. (This fixed cost is incurred
only if the producer turns on the machine.) Answer the questions above for this
case.
(e) Suppose the firm (in the case of second technology having a fixed cost of 20) is a
monopolist facing a market demand described by q = 56 – 2p where p is the unit
price of the firm's output. What would be the market price of this good?

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