ECO 1004 – Mathematics for Economics and Business
Summative Assignment 2
Brief and guidelines
The maximum grade of this assignment is 100.
• This assignment carries a 30% weight of the final grade for this module.
• Submit one single document and not lots of different files.
1. Assess the following functions (15 points):
a. Find the stationary points.
b. Determine whether the stationary point is a maximum or minimum.
c. Draw the corresponding curves, it can be in the same graph.
f ‘ (x) = x²+6x + 2 2. f ‘ (x) = 10x – 2x² + 5
2. A firm has the following short-run production function. 0 = 30L² – 0.5 L³ − (15 points).
a. Make a table with two columns: Production and Labour.
b. Add a third column to the table with the marginal product of labour.
c. Graph the values that you estimated for the production function and the marginal product of labour.
3. A Firm has the following production function Q = 20L – 0.4L² (20 points)
a. Using differential calculus find the unit of labour that maximises the production.
b. Estimate function of Marginal product of labour.
c. Obtain the Average product of labour.
d. Find the point in which marginal product of labour is equal to the average cost.
A firm has the following average cost AC = 200 + 2Q – 36. (20 points)
Q
a. Find the stationary point and determine if it is a maximum or a
minimum.
b. Find the marginal cost function.
5. A firm has the following demand function P = 60 – 0.5Q and its total cost are defined by TC = 13 + Q. (20 points).
a. Find the maximum revenue.
b. Find the production to optimise the profit.
c. Verify if that the marginal revenue and marginal cost are the same at
the profit maximising production level.
6. From the point of view of the firm, what decisions criteria have been found relevant in the analysis of production and profit. (10 points)
