Summative Assignment 1
Brief and guidelines
• Solve all of the following questions.
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. Consider market supply curve which passes through the intercept and from which the market equilibrium data is known, this is, the price and quantity of equilibrium PE = 50 and QE=2000. (20 points)
a. Considering those two points, find the equation of the supply.
b. Draw a graph of this line.
2. Considering the previous supply line, determine if the following demand function corresponds to the market demand equilibrium stated above. QD = 3000 – 2p (15 points)
3. The production function of a firm is described by the following equation Q = 10,000L− 3L² where L stands for the units of labour. (20 points).
a) Draw a graph for this equation. Use the quantity produced in the y-axis, and the units of labour in the x-axis.
b) What is the maximum production level?
c) How many units of labour are needed at that point?
4. Solve the following system of equations (10 points).
50x +20y =1800
10x + 3y =300
5. Consider the demand and supply functions for the notebooks market. (20 Points).
QD =10,000−100p
Qs=900p
a. Make a table with the corresponding supply and demand schedule.
b. Draw the corresponding graph.
c. Is it possible to find the price and quantity of equilibrium with the graph method?
d. Find the price and quantity of equilibrium by solving the system of equations.
6. Supply and demand functions show different relationship between the price and quantities supplied and demanded. Explain the reason for that relation. (15 points).
Summative assignment – Part Two:
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.
1. f ‘ (x) = x²+6x + 2 2. f ‘ (x) = 10x – 2x² + 5
2. A firm has the following short-run production function.
Q = 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.
4. 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)
