Suppose the process of producing light bulbs is described by the function q = 2KL2, where...

Suppose the process of producing light bulbs is described by the function q = 2KL2, where q is the number of light bulbs produced, K is the number of capital inputs,and L is the number of units of labor. Suppose the price of capital is $5 per hour, the price of labor is $10 per hour and 16 units of output are produced.
a) Write down the Lagrangian as a function of K, L and λ.
b) Using the Lagrangian framework of cost minimization, show the mathematical relationship between K and L.

c) Whatistheminimumcostofproducing16unitsofoutput? Istheminimumcostequalto30 dollars? Illustrate your calculations

Solutions

Expert Solution

Rahul Sunny answered 1 week ago

Next > < Previous

Related Solutions

Suppose the process of producing lightweight parkas by Polly’s Parkas is described by the function q...

Suppose the process of producing lightweight parkas by Polly’s Parkas is described by the function q = 10K^0.7(L - 40)^0.3 where q is the number of parkas produced, K the number of computerized stitching-machine hours, and L the number of person-hours of labor. In addition to capital and labor, $15 worth of raw materials is used in the production of each parka. 1. Write total cost function of producing parkas in terms of the quantity produced, and labor and capital...

A factory producing light bulbs has made a recent change in the production process that will...

A factory producing light bulbs has made a recent change in the production process that will be less costly. The fear is that the mean life of the bulbs produced under the new process may be lower than it was before the change. Based upon historical records, it is known that the average lifetime of the bulbs produced before the change was 400 hours. The engineers in the plant are confident that only the mean might be affected by the...

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...

Compact fluorescent bulbs are much more efficient at producing light than are ordinary incandescent bulbs. They...

Compact fluorescent bulbs are much more efficient at producing light than are ordinary incandescent bulbs. They initially cost much more, but last far longer and use much less electricity. According to one study of these bulbs, a compact bulb that produces as much light as a 100 W W incandescent bulb uses only 23.0 W W of power. The compact bulb lasts 10000 hours, on the average, and costs $ $ 11.00, whereas the incandescent bulb costs only $ $...

1. Suppose that the market demand is described by P = A – B(Q+q) where P...

1. Suppose that the market demand is described by P = A – B(Q+q) where P is the market price, Q is the output of the incumbent firm, and q is the output of the potential entrant to the market. The incumbent’s total cost function is C(Q) = c1Q, whereas the cost function of the entrant is C(q) = c2q+F. a. If the entrant firm observes the incumbent producing Q* units of output and expects this output level to be...

Suppose that the cost of producing q appliances is c(q)=200-q+0.96q^2 and the demand function is given...

Suppose that the cost of producing q appliances is c(q)=200-q+0.96q^2 and the demand function is given by q=400-25p. Develop the total revenue, total cost (if not given), and profit functions. Explain these functions in few sentences. Compute the point elasticity of demand. Find the intervals where the demand is inelastic, elastic, and the price for which the demand is unit elastic. Find the quantity that maximizes the total revenue and the corresponding price. Interpret your result. Find the quantity that...

Suppose the production function of PowerGuns Co. is given by Q = 25LK where Q is...

Suppose the production function of PowerGuns Co. is given by Q = 25LK where Q is the quantity of guns produced in the month, L is the number of workers employed, and K is the number of machines used in the production. The monthly wage rate is $3,000 per worker and the monthly rental rate for a machine is $6,000. Currently PowerGuns Co. employs 25 workers and 40 machines. Assume perfect divisibility of labor and machines. What is the total...

Light Bulbs A red light bulb has been flashing forever, according to a Poisson process with...

Light Bulbs A red light bulb has been flashing forever, according to a Poisson process with rate r. Similarly, a blue bulb has been flashing forever, according to an independent Poisson process with rate b. Let us fix t to be 12 o'clock. 1 What is the expected length of the interval that t belongs to? That is, find the expected length of the interval from the last event before t until the first event after t. Here, an event...

4. Suppose a firm’s technology is described by a production function where the quantity produced is...

4. Suppose a firm’s technology is described by a production function where the quantity produced is equal to the square root of capital times labor (that is, Q = √(L●K) a. Using graph paper, draw the isoquant for output = 8 units. b. Suppose the firm has $128 to spend on its variable inputs and the price of L and K is $8. On the same graph on which you drew the isoquant, draw the isocost line. What is the...

Suppose soft drink production at bottling plant is described by the production function: ? =??^?.? where...

Suppose soft drink production at bottling plant is described by the production function: ? =??^?.? where y is the number of cases of soft drinks produced and x is the number of hours of labor hired. We also assume the wage for labor is r, price for soft drink is p and fixed costs is $1,000. How many cases of soft drinks will be produced with 4 hours of labor? Find each of the following if 4 hours of labor...

Subjects