1. Do the following functions exhibit increasing, constant, or decreasing returns to scale? What happens to the marginal product of each individual factor as that factor is increased, and the other factor is held constant?
a. q = A K 0.2L0.8
b. q = L 0.5 + K 0.75
2. Suppose a firm has the following information:
q = KL
MPL = ( K/L)1/2
MPK = (L/K)1/2
w = 4
r = 2
The firm wants to produce 100 units. Find the cost minimizing combination of capital and labour.
3. A firm's total cost function is given by the equation
TC = 4000 + 5Q + 10Q2
The firm's marginal cost is given by MC = 5 + 20Q
Determine the quantity that minimizes average total cost. Discuss your answer and your rationale.
4. The market demand for a type of carpet known as KP-7 has been estimated as:
P = 40 - 0.25Q
where P is price ($/yard) and Q is the rate of sales (hundreds of yards per month). The market supply is expressed as:
P = 5.0 + 0.05Q
A typical firm in this market has a total cost function given as:
C = 100 - 20.0Q + 2.0Q2
MC = 4q - 20
a) Determine the equilibrium market output rate and price.
b) Determine the output rate for a typical firm.
c) Determine the rate of profit/loss earned by the typical firm.
5. At McDonalds University, the demand for textbooks is represented by:
P = 80-10Q
The supply for textbooks is represented by:
P = 10Q
where quantity is measured in thousands of textbooks
a) Without any intervention in the market, what is the equilibrium price and quantity,
b) Suppose that the university's board of governors imposes a price ceiling of $30 on textbooks. Calculate the values of consumer surplus, producer surplus and deadweight loss resulting from the price ceiling. Use a diagram to illustrate your results.
6. Conigan Box Company is a monopolist in the cardboard box industry. Its cost functions and demand functions are as follows:
C = 100 - 5Q + 3Q2
P = 175 - 2Q
MC = -5 + 6Q
MR = 175 - 4Q
where Q is the quantity of cardboard boxes and P is the price per box.
a) What price should Coningan Box Company set to maximize profit and how much output should it produce? How much profit will it earn?
b) What would output be if Coningan Box Company was forced to act like a perfectly competitive firm?
c) With a diagram, show the welfare implication of forcing Conigan Box Company to act like a perfect competitor.
7. In an unregulated competitive market, supply and demand have been estimated as follows:
Demand: P = 25 - 0.10Q
Supply P = 4 + 0.116Q
where P represents unit price in dollars and Q represents the number of units sold per year.
a) Calculate the annual aggregate consumer surplus.
b) Calculate the annual aggregate producer surplus
c) Define what producer surplus is.
8. The Wild West Saloon charges women (W) less than men (M). The bartender whose cost function is given by C + 30 + 2Q separates his customers by gender into two distinct markets:
100Pw = 800 - 0.75Qw
100Pm = 900 - 0.50Qm
where MRm = 9 - 0.01Qm, MRw = 8 - 0.015Qw, MCm = 2, MCw = 2, and Qw + Qm is the aggregate demand (Q) for drinks. Also assume that the bartender acts like a monopolist.
a) How much will the bartender charge men and women for drinks?
b) Suppose that price discrimination by gender is illegal in this area. By how much does the bartenders's profits fall since he/she is unable to price discriminate? Show your work. Note: the aggregate demand for drinks is given be P = 8.6 - 0.003Q (MR = 8.6 - 0.006Q)