Initially suppose that both countries have the same production function, namely q = K.3L.7. For this production function, MPL = .7K.3L-.3 and MPK = .3K.-7L.7.
Derive (with all steps shown) the long-run total cost function for each country. (Given that both countries have the same production function, one derivation will do, and then simply write out the two cost functions, one for each country. Of course, the variables in the cost function for Nepal will have “n” subscripts, and for the U.S. “us” subscripts, though sometimes as for output level in the next sentence, the variables may have the same value.)
Make explicit use of the resulting functions to prove that for any given output level, the total cost of producing that output level in Nepal is less than the total cost of producing it in the U.S.

(b) Now suppose that there is a “technology coefficient” A in the production function for each country, so that the production function is AnK.3L.7 for Nepal and analogously for the U.S., and where An < Aus . (This sort of technology coefficient is referred to as “factor-neutral”.) Assume that for any production function that has a technology coefficient, A > 1.)
For a production function of the form q = AK.3L.7, the marginal products are MPL = .7AK.3L-.3 and MPK = .3AK-.7L.7.
With explicit reference to the steps in the derivation of the cost functions in part (a), show rigorously how the technology coefficients enter into the respective cost functions of the two countries.
Hint: You may find that the technology coefficient “cancels out” in some step in the derivation. That does not mean that it cancels out in every step of the derivation.

(c) Making rigorous use of the cost functions derived in part (b), (that is, the cost functions for the two countries after you have rigorously introduced the technology coefficients), discuss again how the cost of production of any given quantity of gravel in Nepal compares to that in the U.S.

  1. 👍
  2. 👎
  3. 👁

Respond to this Question

First Name

Your Response

Similar Questions

  1. history

    What impact did industrialization have on imperialism? Developing European nations needed to conquer foreign territory to compete with industrialized nations. Increased production led to a surplus in manufactured goods and a need

  2. Math

    The cost of producing x units of a certain commodity is given by P(x)=1000+ int(MC(s))ds from 0 to x, where P is in dollars and M(x) is marginal cost in dollars per unit. A. Suppose the marginal cost at a production level of 500

  3. Math

    2. The cost of producing x units of a certain commodity is given by Px  1000  0 x MCsds, where P is in dollars and Mx is marginal cost in dollars per unit. A. Suppose the marginal cost at a production level of 500 units is

  4. math

    Suppose the total cost function for manufacturing a certain product C(x) is given by the function below, where C (x) is measured in dollars and x represents the number of units produced. Find the level of production that will

  1. math

    Suppose the cost function associated with a product is C(x) = cx + F dollars and the revenue function is R(x) = sx, where c denotes the unit cost of production, s the unit selling price, F the fixed cost incurred by the firm, and

  2. Social Studies

    What is one way that the low wages paid to workers in developing countries has had a negative effect on developed countries? A. Workers in developed countries have experienced job loss. B. Profits for multinational corporations

  3. History

    What are the similarities between the history of Costa Rica and the US? There is more than one correct answer choice. Be sure to select all that apply. A)The army was abolished in both countries. B)The constitutions of both

  4. History

    Select the correct response from the drop-down menu. When countries in this region gained independence, they wrote new constitutions, but in some cases citizens have little freedom because a. the countries do not protect the

  1. Math

    The revenue function for a production by a theater group is R(t)= -50t^2+300t, where t is the ticket price in dollars. The cost function for the production is C(t)= 600-50t. Determine the ticket price that will allow the

  2. Math

    The daily total cost (in dollars) incurred by Trappee and Sons for producing x cases of TexaPep hot sauce is given by the following function. (a) Find the average cost function C. C = ? (b) Find the level of production that

  3. economics

    This table shows the number of labor hours required to produce a digital camera and a bushel of wheat in China and South Korea. Digital Camera Wheat (bushels ) Quantity of Digital Camera Quantity of Wheat China 100 hours 5 hours

  4. social studies

    How has the elimination of trade barriers affected the movement of goods among member countries of the European Union? A. Member countries are able to produce all the goods they need. B. Goods can move freely among member

You can view more similar questions or ask a new question.