You manage a plant the mass produces engines by teams of workers using assembly machines. The technology is summarized by the production:

q = 5KL

Where q is the number of engines per week, K is the number of assembly machines and L is the number of labor teams. Each assembly machine rents for r = 10,000$ per week and each team costs w = 5,000$ per week. Engine costs are given by the cost of labor teams and machines, plus 2,000$ per engine for raw materials. Your plant has a fixed installation of 5 assembly machines as part of its design at the current moment (short run).

a) What is the short run production function?
b) What is the total cost function for your plant to produce q engines (in terms of q only)?
c) What are average and marginal costs for producing q engines in the short run?
d) How many teams are required to produce 250 engines? What is the average cost per engine at this output?

Solution Preview

a) What is the short run production function?

In a short run production function either K or L is fixed. Since you are told that your capital if fixed, your short run production function in this case is q = 25L.

b) What is the total cost function for your plant to produce q engines (in terms of q ...

Rewrite the estimated productionfunction in the form of a power function
Find the marginal product of capital, labor, and gasoline at K=200, L = 400, G = 4,000
See attached file for full problem description.

A firm has a costfunction given by the following:
c(w1, w2, y)= w1w2y^2/(w1+w2)
where the wi's are the prices of the factors (inputs) x1 and x2 respectively, and y is output.
a) Is this a legitimate costfunction?
b) Find the firm's productionfunction, y= f(x1, x2).
c) From the costfunction derive the firm's

Suppose that the Johnson Company has the following productionfunction:
Q = L × C
The price of labor (L) is $20 per unit and the price of capital (C) is $50/unit. How much labor and capital should Johnson employ to produce 200,000 units? What is the total cost of production?

Consider a productionfunction of the form F(K,L)=(K^(-a)+L^(-a))^(-1/a).
(a) Is this function homogeneous?
(b) Does it display increasing, constant or decreasing returns to scale?
(c) Let G be a differentiable function. Find an expression for G(K+g,L+h) by taking a first-order Taylor expansion of G about (K,L).
(d)

I believe that fast food restaurants show short run productionfunction because of a one fixed input, capital. However, I need to elaborate more and produce the productionfunction equation Q=F (L,K,M...) Can you please help?
Also on a fast food restaurant like McDonalds, fixed and variable cost are fixed is capital, build

The difference between the short-run and the long-run productionfunction is:
a. three months or one business quarter.
b. the time it takes for firms to change all production inputs.
c. the time it takes for firms to change only their variable inputs.
d. more information is required to answer this que

1) If a country's labor is paid a total of $6 billion, its capital is paid a total of $2 billion, and profits are zero, what is the level of output?
2) Consider a productionfunction that omits the stock of natural resources. When, if ever, will this omission have serious consequences?
3) Consider a production functio

2. Assume the ProductionFunctionfor Hamburgers is Q = 4L^.50K.^33. where Q is the quantity of hamburgers, L is the number of workers employed and K is number of grills.
a. What is the quantity of hamburgers produced when the company employs 64 workers & 36 machines?
b. Continue to assume the input mix given above—