Now assume there is production in the economy. What is the relation between the marginal rate of substitution and the marginal rate of transformation in a general competitive equilibrium? Derive such relation and explain the intuition behind it.
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Now assume there is production in the economy. What is the relation between the marginal rate of substitution and the marginal rate of transformation in a general competitive equilibrium? Derive such relation and explain the intuition behind it.
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- Assume that you are studying an economy which produces two goods, x and y, using two factors of production, capital K and labour L. The economy’s overall quantities of the two factors are given, and the capital intensity (the capital-to-labour ratio) in the production of y is always higher than the capital intensity in the production of x. At present there is an excess supply of y. Explain and illustrate graphically what will happen in the long run to:1) Prices of goods and production.2) factor prices and factor use intensities in each sector.5. Suppose food (F) and clothing (C) are produced using only labor. The production functions are given by: F = (LF)0.5 C = 0.5(Lc)0.5 Where LF is labor devoted to food production and Lc is labor devoted to clothing production. Labor supply is fixed at 100. Suppose society's preferences can be represented by: U(F,C) = (FC)0.5 Solve for the equilibrium outputs of food and clothing and for the relative price of food (PF/ Pc). LF + Lc = 100Consider the production function of a competitive economy: F (K, L, A) = min (K"L1-a, A), Where K is capital, L is labor, a is some number between zero and one, and A is air. + Capital, labor, and air are in fixed supply. - 1. Give an intuitive explanation of this production function. What role does air play? How does air affect the level of production? 2. Write out the formula for the equilibrium price of capital, labor, and air. 3. Is air necessary for production? Explain how air in this economy could be free despite being a necessary input into the production process? t
- In the Heckscher-Ohlin (H-O) model, Explain with the help of a graph the effect of an increase in the relative price of a labor-intensive good on input choice.Suppose pigs (P) can be fed corn-based feed (C) or soybean-based feed (S) such that the production function is P=2C+5S. If the price of corn feed is $4 and corn feed is on the horizontal axis, and the price of soybean feed is $5 and soybean feed lies on the vertical axis, what is expansion path? the horizontal axis Oa. Ob. Oc. S=2C/5 C. d. C=5S/2 the vertical axisFlorida citrus growers say that the recent crackdown on illegal immigration is increasing the market wage rates necessary to get their oranges picked. Some are turning to $100,000 to $300,000 mechanical harvesting machines known as “trunk, shake, and catch” pickers, which vigorously shake oranges from the trees. If widely adopted, how will this substitution affect the demand for human orange pickers? What does that imply about the relative strengths of the substitution and output effects?
- 11 7. Suppose that for some reason we were interested in studying solutions to the following problem: A firm produces a single output y from N inputs x = (x1 , • • • , xN) . The firm is given a certain budget that it can spend on inputs, and the firm produces as much output as it can given that budget. Letting B be the budget and supposing the firm is described by a production function f (x ) and that the firm is competitive and faces factor prices w, we can define y* (w, B) = max{f (x) :w ·x ::.; B}. Devise a theory concerning this problem in the spirit of the results we have given concerning partial derivatives of y* and solutions to the problem just posed.Explain the absence of economic profit in a purely competitive, static economy. Realizing that the major function of profit is to allocate resources according to consumer preferences, describe the allocation of resources in such an economy.Question 13 5 pts For the production function y = 4x1+ 3x2, which of the two inputs is more productive when x1 is 10 and x2 is 10? X1 X 2 neither; for this situation, they have equal marginal products cannot tell from the above information Question 14 5 pts Given the production function y = x1 1/3 x,1/3, what is the marginal physical product of x2 when x1 is 5 and x2 is 5? O 0.75 37 0.19 O 1.11
- Microeconomics 2 - Factor Market - Pareto Optimum Consider an economy in which only 2 factors are capital (K) and labor (L) whose total supply is 100 labor and 100 capital. They are used by only firm that produces only 2 final goods X and Y. The technology describing the production process of each of goods is described by the following production functions: X = 5 Lx + 3 Kx and Y = 1/3 Ly Ky It’s known that the factors have been allocated in such a way that the initial endowment is: Kx = 75; Lx = 85; Ky = 25 and Ly = 15. With these data we ask: Obtain the contract curve corresponding to the production of this economy. Does the starting point constitute a PARETO OPTIMUM? Represent the available information in an Edgeworth Box. Obtain the production possibilities frontier (PFC) curve. Locate the initial endowment THANKS :Dcould you write the solution with pen and paper please?3) Ajax, Inc. assembles gadgets. It can make each gadget either by hand or with a special gadget- making machine. Each gadget can be assembled in 15 minutes by a worker or in 5 minutes by the machine. The firm can also assemble some of the gadgets by hand and some with machines. Both types of work are perfect substitutes, and they are the only inputs necessary to produce the gadgets. a) Write down the equation of the firm's production function for the firm. Let G be the number of gadgets assembled, M the number of hours the machines are used, and I the number of hours of labor. b) It costs the firm $30 per hour to use the machine and $10 per hour to hire a worker. The firm wants to produce 120 gadgets. What is the cost-minimizing input quantities? Illustrate your answer with a clearly labeled graph. d) Derive the expression for the long-run total cost that the firm incurs, as a function of q. Represent it in a diagram.