The production function of a good is f(L,M)=4L1/2 M1/4, where L is the number of units...

The production function of a good is f(L,M)=4L1/2 M1/4, where L is the number of units of labor and M is the number of machines used. The cost of labor is $20 per unit and the cost of machines is $10 per unit. If the firm decides to produce Q units of output, (1) Does the production function exhibit increasing returns to scale? Why? (2) Get the conditional factor demand for L and M. (3) If there is a set-up cost at $1000. Find the total cost of producing Q units of output using the answer from (2). (4) Find the average total costs function and marginal costs function?

Expert Solution

Rahul Sunny answered 1 day ago

3. the production function is f(L, M)=4*(L^1/2) (M^1/2), where L is the number of units of...

3. the production function is f(L, M)=4*(L^1/2) (M^1/2), where L is the number of units of labor and M is the number of machines used. If the cost of labor is $49 per unit and the cost of machines is $25 per unit, then how much will be the total cost of producing 7 units of output ?

Consider the production function F(L,K) = L^2/3 K^2/3 . (f) Does this production function exhibit increasing,...

Consider the production function F(L,K) = L^2/3 K^2/3 . (f) Does this production function exhibit increasing, decreasing or constant returns to scale? Explain. (g) Find the total cost, average cost and marginal cost of producing y units of output. Is the average cost increasing or decreasing in y? Is the marginal cost higher or lower than the average cost? Question 2 The production of magic chairs requires only two inputs: seats (S) and legs (L) (no other inputs are required...

The production function of an economy is F(K,L) = 20(K0.5L0.5), where L is labour and K...

The production function of an economy is F(K,L) = 20(K0.5L0.5), where L is labour and K is capital with L = 400 and K = 400. What type of returns to scale does this production function exhibit?

Suppose a production function is given by F ( K , L ) = K^(1/2) L^(1/2), the...

Suppose a production function is given by F ( K , L ) = K^(1/2) L^(1/2), the price of capital “r” is $16, and the price of labor “w” is $16. a. (5) What combination of labor and capital minimizes the cost of producing 100 units of output in the long run? b. (5) When r falls to $1, what is the minimum cost of producing 100 pounds of pretzels in the short run? In the long run? c. (5) When...

Suppose a production function is given by F ( K , L ) = K 1 2...

Suppose a production function is given by F ( K , L ) = K 1 2 L 1 2, the price of capital “r” is $16, and the price of labor “w” is $16. a. (5) What combination of labor and capital minimizes the cost of producing 100 units of output in the long run? b. (5) When r falls to $1, what is the minimum cost of producing 100 pounds of pretzels in the short run? In the long...

2. Suppose a production function is given by F ( K , L ) = K 1...

2. Suppose a production function is given by F ( K , L ) = K 1 2 L 1 2, the price of capital “r” is $16, and the price of labor “w” is $16. a. (5) What combination of labor and capital minimizes the cost of producing 100 units of output in the long run? b. (5) When r falls to $1, what is the minimum cost of producing 100 pounds of pretzels in the short run? In the...

Suppose that output Q is produced with the production function Q = f(K;L), where K is...

Suppose that output Q is produced with the production function Q = f(K;L), where K is the number of machines used, and L the number of workers used. Assuming that the price of output p and the wage w and rental rate of capital r are all constant, what would the prot maximizing rules be for the hiring of L and K? (b) What is theMRTSK;L for the following production function: Q = 10K4L2? Is this technology CRS, IRS or...

Suppose that output Q is produced with the production function Q = f(K,L), where K is...

Suppose that output Q is produced with the production function Q = f(K,L), where K is the number of machines used, and L the number of workers used. Assuming that the price of output p and the wage w and rental rate of capital r are all constant, what would the proﬁt maximizing rules be for the hiring of L and K? (b) What is the MRTSK,L for the following production function: Q = 10K4L2? Is this technology CRS, IRS...

The technology available allows to produce a good according to the production function F(L,K)=[(L-3)K]1/3 if L≥3...

The technology available allows to produce a good according to the production function F(L,K)=[(L-3)K]1/3 if L≥3 and K≥0, and F(L,K)=0 if L<3. The market demand for this good is D(p)=90/p. The prices of labor and capital are w=1 and r=9, respectively. A. (12 points) Describe the cost minimization problem of a firm with this technology, and calculate its conditional factor demands. Also, calculate the firm's total, average and marginal cost functions. B. (10 points) Calculate la supply of a competitive...

Suppose Noah and Naomi's short-run weekly production function for garden benches is F(L)=min{0,L−3},F(L)=min⁡{0,L−3}, where L...

Suppose Noah and Naomi's short-run weekly production function for garden benches is F(L)=min{0,L−3},F(L)=min⁡{0,L−3}, where L represents the number of hours of labor employed. The wage rate is $12 an hour. For non-negative amounts of output, what is their short-run cost function? C = 36 + 12Q. C =12 +36Q. C =12Q. C = 36Q. C =36 - 12Q.

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