Microeconomics (9th Edition) (Pearson Series in Economics)
Microeconomics (9th Edition) (Pearson Series in Economics)
9th Edition
ISBN: 9780134184241
Author: Robert Pindyck, Daniel Rubinfeld
Publisher: PEARSON
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Chapter 6, Problem 10RQ
To determine

The diminishing marginal rate of technical substitution.

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Prunella raises peaches. She uses L units of labor, and T units of land to produce peaches. Her production function is f(L, T)= L1/2T 1/2 A: Write the equation and plot the isoquant for the output quantity 4. B: What is the returns to scale of this production function? C: Find the marginal products of labor and land. What is the rate of technical substitution between land and labor? D: In the short-run, Prunella cannot vary the amount of land she uses. Plot the output as a function of labor only for the fixed level of land of T=1. E: Find the marginal product of labor from L=4 and show it on the graph. Is the marginal product of labor diminishing, constant or increasing in labor? F: Suppose wages are constant and equal w, fixed costs are zero. Find the short-run profit maximizing level of labor for T=1.   Please see the attached photo
For each of the following examples, draw a representative isoquant. What can you say about the marginal rate of technical substitution in each case? a) A firm finds that it can always trade two units of labor for one unit of capital and still keep output constant. b) A firm requires exactly two full-time workers to operate each piece of machinery in the factory.
Assume a technological change in production that makes both inputs, capital and labour more productive, but that increases more the productivity of capital than the productivity of labour. Explain how this change translates into the shape of the isoquant curves and in the marginal rate of technical substitution. Provide graphs to illustrate your arguments.
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