1. Firm Fiat Lux, a light bulb company, has the production function q = 2L 0.5K...

1. Firm Fiat Lux, a light bulb company, has the production function q = 2L 0.5K 0.5. If it has to make 800 light bulbs, and the price of one unit of capital is 40 and the price of one unit of labor is 25, use the Lagrangian method to find the marginal cost of production.

a 125.9867
b. 31.6228
c. 1.667
d. 25.7371

2.

About the Lagrangian method, select the correct statement:

a. We can use it to solve firm's cost minimization problems, but not consumer's utility maximization problems.

b. We can use it to solve consumer's utility maximization problems, but not firm's cost minimization problems.

c. We cannot use it to solve any kind of optimization problem.

d. We can use it to solve both consumer's utility maximization and firm's cost minimization problems.

3. Firm Fiat Lux, a light bulb company, has the production function q = 2L ^0.5K ^0.5. If it has to make 800 light bulbs and price of one unit of capital is 40 and price of one unit of labor is 25, which is the Lagrangian function corresponding to this firm's cost minimization problem?

a. ℒ(L, K, λ) = 40K + 25L + λ(800 - 2L^0.5K^0.5 )

b. ℒ(L, K, λ) = 2L^0.5K^0.5 + λ(800 - 40K - 25L)

c. ℒ(L, K, λ) = 2L^0.5K^0.5 + λ(25298 - 40K - 25L)

d. None of the above

Expert Solution

Rahul Sunny answered 1 year ago

2. A firm has production function Q = k^1/2L^1/2 and faces a wage for the labor...

2. A firm has production function Q = k^1/2L^1/2 and faces a wage for the labor input w = 1 and a rental price of capital r = 9 a. The policy of the Federal Reserve brings the rental price of capital to r = 4 Graph the change of the cost minimizing equlibrium explaining the type of substitution that is happening. b. Compute the new cost function. Suppose a monopoly and show graphically if after this change in the...

craft corp's production function is given by q = 5min(K, 2L),where q is the quantity...

craft corp's production function is given by q = 5min(K, 2L), where q is the quantity produced and K and L are the amounts of capital and labor input. Input prices are r = 2 and w = 6.a) find the long run cost functionb) draw the isoquants and isocost and show the equilibrium when q = 2000. what is the total cost to produce q = 2000? what is the labor cost to produce q = 2000? what is...

craft corp's production function is given by q = 5min(K, 2L), where q is the quantity...

craft corp's production function is given by q = 5min(K, 2L), where q is the quantity produced and K and L are the amounts of capital and labor input. Input prices are r = 2 and w = 6. a) find the long run cost function b) draw the isoquants and isocost and show the equilibrium when q = 2000. what is the total cost to produce q = 2000? what is the labor cost to produce q = 2000?...

Short questions: a. A firm has production function f(K, L) = 2L + 3K. The price...

Short questions: a. A firm has production function f(K, L) = 2L + 3K. The price of L is w and the price of K is r. Derive the cost function of the firm. b. A firm in a competitive industry takes account of the fact that the demand curve it faces has a negative slope. True or false? c. A profit-maximizing firm continues to operate even though makes negative profits. It sells its product at a price of $100....

Suppose a short-run production function is described as Q = 2L – (1/800)L2 where L is...

Suppose a short-run production function is described as Q = 2L – (1/800)L2 where L is the number of labors used each hour. The firm’s cost of hiring (additional) labor is $20 per hour, which includes all labor costs. The finished product is sold at a constant price of $40 per unit of Q. d. Suppose that labor costs remain unchanged but that the price received per unit of output increases to $50. How many labor units (L) will the...

1.A price-taking firm Bikes Inc makes and sells bicycles. Bikes Inc uses the production function q=(k+2l)^(1/3)....

1.A price-taking firm Bikes Inc makes and sells bicycles. Bikes Inc uses the production function q=(k+2l)^(1/3). Input prices are w=2 and v=3 for labor and capital respectively. Given that the firm uses initial amount of capital k=12 . compute the firm's short-run cost function. To verify that your have correct short-run cost function, calculate the short-run cost of producing 8 bicycles. Consider that the firm uses initial amount of capital k = 12 , and the firm faces the price P...

27) A firm has a production function Q = KL, where Q is the quantity of...

27) A firm has a production function Q = KL, where Q is the quantity of output, K is the amount of capital and L is the amount of labor. MPL=K and MPK=L. a) Suppose that capital is fixed at K=10 in short run. In this case, the marginal product of labor is MPL=10. Does this production function exhibit diminishing marginal returns to labor? b) Suppose that in the short run, K is fixed at 10. The interest rate is...

A firm has a production function Q = KL, where Q is the quantity of output,...

A firm has a production function Q = KL, where Q is the quantity of output, K is the amount of capital and L is the amount of labor. MPL=K and MPK=L . a) Suppose that capital is fixed at K=10 in short run. In this case, the marginal product of labor is MPL=10. Does this production function exhibit diminishing marginal returns to labor? b) Suppose that in the short run, K is fixed at 10. The interest rate is...

A firm producing baseball bats has a production function given by Q = 2K1/2L 1/2. In the short-run, the firm’s amount of capital equipment is fixed at K = 100.

A firm producing baseball bats has a production function given by Q = 2K1/2L 1/2. In the short-run, the firm’s amount of capital equipment is fixed at K = 100. The rental rate for capital is r=$1, and wage rate for labor is w = $4.a. Calculate the firm’s short-run total cost curve.b. Calculate the firm’s short run average variable cost curve.c. The firms short-run marginal cost curve is given by MC= Q/50. What is total cost, marginal cost, and...

Suppose a firm has the production function, Q = 12KL. It has a contract to produce...

Suppose a firm has the production function, Q = 12KL. It has a contract to produce 144 units of output per day. One way to do is to use 3 units of capital (K) and 4 units of labor (L). Suppose a unit of labor costs $2 (wage = w) while a unit of capital costs $3 (r). What is the slope of the isocost line? A) 2/3 B) 1/4 C) 1/3 D) 3/2 At this combination of inputs, is...

Question