Assignment 1 Solution

Assignment 1 Solution - Name_ Food & Resource Economics...

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Name______________________________ Due date : 09/15/10 Solutions for Assignment #1 EXPRESSING RELATIONSHIPS —SCHEDULES AND GRAPHS WITH RESPECT TO THE PRODUCTION AND COST FUNCTION Part I In this exercise we are going to look at one of the fundamental relationships in microeconomics, namely the production function. The concept of this assignment is to familiarize yourselves with the basic instruments used in analyzing a production function. As with most economic analyses we begin with a simple model based on a number of assumptions and then move on to more complex models created by relaxing some of those assumptions. In the most simple model we will assume that a single input (factor, resource) is used to produce a single output (product, good). Multiple inputs and outputs will generalize the production model. One Input model A production function, or a total product function stipulates that total product is a function of the amount of the variable input used in combination with fixed inputs: ) | ( F V f TP = = ) ( L f Q = where: TP = units of total (physical) product V = units of the variable input used in combination with in this case labor ( L ) F = one unit of the fixed input(s). Definition : A production function is a short-run schedule, graph, or equation showing the relationship between units of the variable input(s) and units of output(s), where units of the variable input(s) and output(s) are both measured per unit of the fixed inputs, ceteris paribus. Definitions : The amount of the output is call total product . Average product is the amount of output per unit of the variable input Marginal product is the change in total product per unit change of the variable input
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Average product is given by: V TP AP = or L L f L Q AP ) ( = = and marginal product represents change in total product per unit change in the variable input, so L Q V TP MP δ = = where the Greek symbol δ (delta) means “change in”. 1. The table on the next page shows a production function for squash expressed as a schedule. Use the formula given above to fill in the blanks on this schedule. Round all calculations to two significant decimal places 1 . Note that the marginal product is placed between two total and average products to emphasize that this is the change between two points. 2. Once the schedule on the next page has been completed, plot and graph the total, average and marginal products on the following page. Because of large differences in the magnitude of the numbers, the total product is graphed on the upper chart while average and marginal product are graphed on the lower chart. Note that both the upper and lower charts share the same horizontal axis. Remember to plot the marginal products between input levels—that is, the marginal product between variable input levels of 3 and 4 should be plotted at 3.5 on the horizontal axis. Now note the following relationships:
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This note was uploaded on 02/10/2011 for the course AEB 3103 taught by Professor Cazanova during the Fall '08 term at University of Florida.

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Assignment 1 Solution - Name_ Food & Resource Economics...

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