A firm faces a production function of twittle-twaps: Q(K,Lp,Ln) = 5*K(2/5)*LP (1/3)*LN(1/5) per hour, where capital (K), production labor (LP), and non-production labor (LN) are input factors used in production. The firm operates in a competitive market, where they are a price taker within the capital & labor markets and its own price (r = 40, wP = 25, wN = 50, P = 20). Answer the following. a. If capital and non-production labor are fixed at K = 32 and LN = 243, what is the general form MPLP and graph Q wrt to LP changing [you do not need to solve for LP yet].
4) A firm faces a production function of twittle-twaps: Q(K,Lp,Ln) = 5*K(2/5)*LP
(1/3)*LN(1/5) per hour, where
capital (K), production labor (LP), and non-production labor (LN) are input factors used in production.
The firm operates in a competitive market, where they are a price taker within the capital & labor
markets and its own price (r = 40, wP = 25, wN = 50, P = 20). Answer the following.
a. If capital and non-production labor are fixed at K = 32 and LN = 243, what is the general form
MPLP and graph Q wrt to LP changing [you do not need to solve for LP yet].
b. Is this production function decreasing, constant, or increasing returns to scale and why.
c. Given the wage of production workers and the price of twittle-twaps, what is the optimal number
of LP to employ to maximize profits and the quantity produced (VMPLP = wP).
d. If the firm can control both K and LP, what does the Isoquant curve look like and its slope in
relative terms if LN is fixed at 243 units [IQ slope = MPLP/MPK].
e. If the manager faces a cost budget of C = $16,550/hour, what are the optimal number of K and
LP to employ to maximize production and the quantity produced, given LN = 243.
f. Generally, what will happen to the optimal number of capital and labor if the cost of renting
capital (r) decreases and why.
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