Mathematics for Economics and Business Summative Assignment 3

Mathematics for Economics and Business Summative Assignment 3

Brief and guidelines

• Solve all of the following questions.
• The maximum grade of this assignment is 100.
• This assignment carries a 40% weight of the final grade for this module.
• Submit one single document and not lots of different files.

1. Consider the following supply and demand schedule of wooden tables.
2. Draw the corresponding graphs for supply and demand.
3. Using the data, obtain the corresponding supply and demand functions.
4. Find the market-clearing price and quantity. (20 Points)

Price                                                                   Supply                                                Demand

(Thousands)

USD)

2. Consider a firm with the following production function

Q = 5000L – 2L² (20 points).

1. Find the maximum production level.
2. How many units of labour are needed at that point.
3. Obtain the function of marginal product of labour (MRL ).
4. Graph the production function and the (MRL .

3. A firm has the following demand function and the average cost

Of P = 200-2Q and the average cost of AC = 100 + 3Q-20 (20points)

 Q

1. Find the profit function.
2. Estimate the marginal cost function.
3. Obtain the production that maximizes the profit.
4. Evaluate the average cost and the marginal cost at the maximising

production level.

4. A firm has the following total cost function TC =100q-5q²+ 0.5q³ (10 points).

1. Find the average cost function.

5. Considering the following supply and demand equations (20 Points):

Qs = 3P – 1

Qd = −2P+q

dP = 0.5(Qd – Qs )

dt

1. Find the expressions. P(t), Qs (t) and Qd (t). When P (0) = 1 , is the system stable or unstable?

1. b) If the constant for the change of excess of demand changes to 0.6, this is:

dP= 0.6(Qd−Qs )

do P(t), Qs (t) and Qd (t) remain the same when P(0)=1?

6. Explain the importance of differential calculus within economics and business analysis (10 Points).