1. A profit-maximizing firm that produces a particular product has two plants.
Cost functions of the facilities are:
a) b) c)
plant 1: TC1 = 0.005q12 + 42q1 + 1700
plant 2: TC2 = 0.1q22 + 2q2 + 25
a)What Marginal Cost(MC) is valid in each facility?
b)Show the Marginal Cost(MC) curves.
c)Please give the total and average costs for a production of 500 units.
d)Please give the total and average costs for a production of 950 units.
2. A monopolist faces the demand as follows:
Price Quantity
16 0
14 1000
12 2000
10 3000
8 4000
6 5000
4 6000
2 7000
0 8000
The company has a fixed cost of 25 000 € and constant marginal costs of 4 per unit.
a) What will be the profit-maximizing quantity, price terms, and how great will be the gain?
b) Assume now that the firm can price discriminate perfectly. How many units are produced then the maximum profit, and what is the maximum profit?
3.
A profit-maximizing firms operating in a perfectly competitive market, where the market price is 80 SEK. Total cost function is:
TC = q2 + 20q + 700
a) How many units should the company produce, and what is the profit?
b) At a cost of 10 per unit produced, the company can differentiate their product compared to their competitors, giving them the opportunity to pursue a more independent pricing policy. Calculate the “new” TC function!
c) After product differentiation the demand for its product might be given by the relation: Q = 100 - 0.625p
Is the product differentiation worthwhile?
4.
5.
What are the respective marginal products? What is the technical rate of substitution?
a) y = x1 + 2x2
b) y = ax1 + bx2 c) y = x11/4x23/4 d) y= (x1+2)(x2+1)
A company is the sole purchaser of labor in the locality, the labor
supply can be described by: W = 10 + 0.1L where W is the daily wage and L is the number of "person days" work. The company's production function can be written: Q = 10L, where Q is output. The demand for these outputs can be described by:
P = 41 - (Q / 1000) where P is the output rate.
a) What is the profit maximizing level of output for the
company?
b) How much manpower is then used?
c) What wages apply in this situation?
d) Which output price prevailing then?
For the following production functions, answering: Are there constant
returns to scale?
6.
a) The profit-maximizing monopolist Alga has the cost function: C (y) = 16y
and meets an (inverse) demand function:
p (y) = 80 – y
What is the maximum profit? Draw a picture and enter the welfare loss in the figure. How large is the welfare loss. Explain the concept of the welfare loss. Finally, assume the introduction of a tax of SEK 4 per unit, what will then the profit-maximizing price become?
b) Another monopolist has the constant marginal cost of £ 10,000 per unit, and faces two separate markets that allow price discrimination, with the (inverse) demand functions:
pa = 40000 - 20q and pb = 25000 - 50q
What pricing is profit maximization? How much does the company gain from a price discriminating behavior?
Cost functions of the facilities are:
a) b) c)
plant 1: TC1 = 0.005q12 + 42q1 + 1700
plant 2: TC2 = 0.1q22 + 2q2 + 25
a)What Marginal Cost(MC) is valid in each facility?
b)Show the Marginal Cost(MC) curves.
c)Please give the total and average costs for a production of 500 units.
d)Please give the total and average costs for a production of 950 units.
2. A monopolist faces the demand as follows:
Price Quantity
16 0
14 1000
12 2000
10 3000
8 4000
6 5000
4 6000
2 7000
0 8000
The company has a fixed cost of 25 000 € and constant marginal costs of 4 per unit.
a) What will be the profit-maximizing quantity, price terms, and how great will be the gain?
b) Assume now that the firm can price discriminate perfectly. How many units are produced then the maximum profit, and what is the maximum profit?
3.
A profit-maximizing firms operating in a perfectly competitive market, where the market price is 80 SEK. Total cost function is:
TC = q2 + 20q + 700
a) How many units should the company produce, and what is the profit?
b) At a cost of 10 per unit produced, the company can differentiate their product compared to their competitors, giving them the opportunity to pursue a more independent pricing policy. Calculate the “new” TC function!
c) After product differentiation the demand for its product might be given by the relation: Q = 100 - 0.625p
Is the product differentiation worthwhile?
4.
5.
What are the respective marginal products? What is the technical rate of substitution?
a) y = x1 + 2x2
b) y = ax1 + bx2 c) y = x11/4x23/4 d) y= (x1+2)(x2+1)
A company is the sole purchaser of labor in the locality, the labor
supply can be described by: W = 10 + 0.1L where W is the daily wage and L is the number of "person days" work. The company's production function can be written: Q = 10L, where Q is output. The demand for these outputs can be described by:
P = 41 - (Q / 1000) where P is the output rate.
a) What is the profit maximizing level of output for the
company?
b) How much manpower is then used?
c) What wages apply in this situation?
d) Which output price prevailing then?
For the following production functions, answering: Are there constant
returns to scale?
6.
a) The profit-maximizing monopolist Alga has the cost function: C (y) = 16y
and meets an (inverse) demand function:
p (y) = 80 – y
What is the maximum profit? Draw a picture and enter the welfare loss in the figure. How large is the welfare loss. Explain the concept of the welfare loss. Finally, assume the introduction of a tax of SEK 4 per unit, what will then the profit-maximizing price become?
b) Another monopolist has the constant marginal cost of £ 10,000 per unit, and faces two separate markets that allow price discrimination, with the (inverse) demand functions:
pa = 40000 - 20q and pb = 25000 - 50q
What pricing is profit maximization? How much does the company gain from a price discriminating behavior?
