Reference no: EM132377558
ECON 3730 The Origins of International Inequality - University of Guelph
Assignment 2
1. For this decision tree question all the information is about costs, so when comparing the expected net present value, you are looking for the decisions with the lowest cost. Also assume all values are already in present value terms. (no discounting required) A forest company is deciding on whether or not to comply with government regulations regarding harvesting practices. The cost of compliance is $110,000. The cost of non compliance involves uncertainty. There is a 70% chance of not being caught in which case the firm avoids all costs. However there is a 30% chance that the firm will be caught. If the firm is caught, there is a 25% chance that the fine will be small. Otherwise the fine will be large. If the fine is small the firm will pay the fine of $200,000. If however, the fine is large, then the firm must decide whether to just pay the fine of $400,000 or fight it in court. If the firm decides to fight the fine, lawyer costs are $50,000 regardless of the outcome. In court there is a 50% chance that the firm will have to pay the $600,000 fine; there is a 30% chance that the firm will have to pay a $220,000 fine and a 20% chance that the firm will not have to pay a fine at all.
Calculate the expected present value of the cost of non compliance. Should the firm comply with the regulation? Show your decision tree.
2. Your firm has capital costs fixed at $400. Labour is the firm's only variable input. Labour is paid $20.25 per hour. You are asked to determine the level of output that will maximize profits, given the following information relating quantity of labour hours and the resulting quantity of output produced. Your firm's output sells for $4.50 per unit.
To present your analysis to the firm, you must prepare the following:
|
Quantity of Labour (hours)
|
Quantity of output
|
|
0
|
0
|
|
2
|
30
|
|
4
|
70
|
|
6
|
100
|
|
8
|
125
|
|
10
|
145
|
|
12
|
160
|
|
14
|
172
|
|
16
|
182
|
|
18
|
190
|
|
20
|
197
|
|
22
|
202
|
|
24
|
206
|
a. A table, giving Total Variable Factor Cost, Fixed Cost, Total Factor Cost, Total Revenue Product, Profits, Marginal Factor Cost, Marginal Revenue Product, Average Total Factor Cost, Average Revenue Product, Marginal Product and Average Product.
b. Plot the Total (physical) product curve.
c. Plot the marginal and average product curves.
d. Plot the Total Factor Cost, Total Variable Factor Cost, Fixed Cost, and Total Revenue Product curves
e. Plot the average total factor cost, average revenue product, marginal factor cost and marginal revenue product curves. Illustrate quantity of output that maximize annual profit. Illustrate the area representing profit on this diagram.
f. How many units of output would you produce maximize profit? What is the value of profit if your recommendation is followed?
g. Indicate the optimal input level and the resulting level of output on the total product curve. Is this the same level of input that maximizes average product?
h. If capital costs decreased to $200, how does your profit maximizing level of labour change? Explain.
i. Starting from the original example, if labour costs increase to $24.75 per hour, how does your profit maximizing level of labour change? Explain using a Marginal Revenue Product and Marginal Factor Cost Curve.
j. Starting from the original example, if the price at which you can sell your output changes to $5.40 how does your profit maximizing level of labour change? Explain using a Marginal Revenue Product and Marginal Factor Cost Curve.
Notes for using excel: Marginal values are plotted at the half unit, which excel cannot do. You can adjust the marginal values that you have calculated by adding two together and dividing by 2. For example, Marginal product from increasing labour from 0 to 2is (30-0)/(2-0) = 15. This is really the value of marginal product at 1 units of labour. Marginal product from increasing labour from 2 to 4 is (70-30)/(4-2) = 20. This is really the value of marginal product at 3 units of labour. So at the quantity of labour =2, Marginal Product must be (15+20)/2 = 17.5. When plotting your diagrams, the column on the far left will be on the x axis, the rest will be plotted on the y axis. YOU HAVE TO USE A SCATTER PLOT!!!!