(25 pts) Nintendo produces Switch and uses three inputs: Labor (L), Gaming Engine (K), and other materials, (M). The production function if Nintendo is given as: Q(K,L,M) KLM The marginal products associated with the production are given as: MPL KM; MPK = LM; MPM=LK = The cost of labor is $5, the cost of renting a gaming engineer is $1, and the cost of the other materials (per unit) is $2. a. (10 pts) Suppose that Nintendo wants to produce Q units of games in time for Tokyo game show. Show how the cost-minimizing quantity of Gaming engines, K, depends on the number of games, Q. Also, show how the cost-quantity is dependent on the quantity of materials, M depends on the quantity of games, Q. b. (3 pts) Find an equation that represents Nintendo's long-run total cost curve. C. (2 pts) Find an equation that represents Nintendo's long-run average cost curve. d. (10 pts) Suppose that Nintendo wants to produce Q games with a fixed number of Gaming Engines equal to 50. Show the cost- minimizing quantity of labor depends on the quantity of games, Q. Show also how the cost-minimizing quantity of materials depends on the quantity of games, Q. e. (5 pts) Find the equation that represents the short-run total cost curve when the number of Gaming engines is fixed at 50. Also, find the equation the associated short-run average cost of Nintendo.
(25 pts) Nintendo produces Switch and uses three inputs: Labor (L), Gaming Engine (K), and other materials, (M). The production function if Nintendo is given as: Q(K,L,M) KLM The marginal products associated with the production are given as: MPL KM; MPK = LM; MPM=LK = The cost of labor is $5, the cost of renting a gaming engineer is $1, and the cost of the other materials (per unit) is $2. a. (10 pts) Suppose that Nintendo wants to produce Q units of games in time for Tokyo game show. Show how the cost-minimizing quantity of Gaming engines, K, depends on the number of games, Q. Also, show how the cost-quantity is dependent on the quantity of materials, M depends on the quantity of games, Q. b. (3 pts) Find an equation that represents Nintendo's long-run total cost curve. C. (2 pts) Find an equation that represents Nintendo's long-run average cost curve. d. (10 pts) Suppose that Nintendo wants to produce Q games with a fixed number of Gaming Engines equal to 50. Show the cost- minimizing quantity of labor depends on the quantity of games, Q. Show also how the cost-minimizing quantity of materials depends on the quantity of games, Q. e. (5 pts) Find the equation that represents the short-run total cost curve when the number of Gaming engines is fixed at 50. Also, find the equation the associated short-run average cost of Nintendo.
Chapter11: Profit Maximization
Section: Chapter Questions
Problem 11.9P
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Transcribed Image Text:(25 pts) Nintendo produces Switch and uses three inputs: Labor (L), Gaming Engine (K), and
other materials, (M). The production function if Nintendo is given as:
Q(K,L,M) KLM
The marginal products associated with the production are given as:
MPL KM; MPK = LM; MPM=LK
=
The cost of labor is $5, the cost of renting a gaming engineer is $1, and the cost of the other
materials (per unit) is $2.
a. (10 pts) Suppose that Nintendo wants to produce Q units of games in time for Tokyo game
show. Show how the cost-minimizing quantity of Gaming engines, K, depends on the
number of games, Q. Also, show how the cost-quantity is dependent on the quantity of
materials, M depends on the quantity of games, Q.
b. (3 pts) Find an equation that represents Nintendo's long-run total cost curve.
C.
(2 pts) Find an equation that represents Nintendo's long-run average cost curve.
d. (10 pts) Suppose that Nintendo wants to produce Q games with a fixed number of Gaming
Engines equal to 50. Show the cost- minimizing quantity of labor depends on the quantity of
games, Q. Show also how the cost-minimizing quantity of materials depends on the
quantity of games, Q.
e. (5 pts) Find the equation that represents the short-run total cost curve when the number of
Gaming engines is fixed at 50. Also, find the equation the associated short-run average cost
of Nintendo.
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