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Assume that a firm has the following short-run production function: q = 10L^0.5 and that the market wage rate is 4.

a. Derive the equations for the marginal and average product of labor.

b. Derive the equations for the firm's short-run marginal and average variable cost curves.

c. What is the equation for the firm's short-run supply curve?

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Darryn D'Souza
Darryn D'SouzaLv10
28 Sep 2019

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Related questions

7) You are a business manager working for a firm in a purely competitive market and you just hired a summer intern who does not understand how to derive the firm's short-run supply curve from the firm's marginal cost curve. Please explain this to the intern.

a) Please explain to the intern how the short-run supply curve is derived from the firm's marginal cost curve.

ii) Please explain why there is a direct relationship between product price and quantity supplied.

Which of these curves is the competitive firm's short-run supply curve:

a. the average total cost curve

b. demand curve above the marginal revenue

c. same as the market supply

d. the marginal cost above the average variable cost curve

A fi? rm produces a product with labor and capital. Its production function
is described by Q = 2L + 3K: Let w and r be the prices of labor and capital,
respectively.

(a) Find the equation for the? firm's long-run total cost curves as a function
of quantity Q, for input prices, w = 1 and r = 1.

(b) Find the equation for the firm's long-run total cost curves as a function of
quantity Q and input prices, w and r (and so as a function of three parameters).

c) Find the solution to the ?firm's short-run cost-minimizationproblem when
capital is fi?xed at a quantity of 5 units (i.e., K = 5), and w = 1and r = 1.
Derive the equation for the? firm's short-run total cost curve as a function of
quantity Q. Graph this curve together with the long-run total cost curve for
the same input prices.

(d) Redo parts a) and c) for w = 1 and r = 2:

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