Economics Homework Help

1. (10) For each of the following, determine whether the technology exhibits increasing,
decreasing or constant returns to scale. You must show your work.
a) ( , ) = 2
1
4
3
4
b) ( ) = 2
3

2. (15) In the following figure, clearly identify the firms’ revenue and costs at the output
price
0
. (You will have to reproduce the figure in your answer sheet.) Would the firm
earn (positive) profits or incur losses? Clearly depict the profits or losses in your diagram.

3. A firm producing hockey sticks has a production function given by: = 2 + ,
where K is the capital inputs and L represents the amount of labor used.
a) (10) Consider the long-run cost-minimization problem of the firm for a given level of
output q. Derive the optimal demand for the two inputs K and L as a function of q
when the unit prices of the two inputs are r and w respectively.
b) (5) Compute the total cost function in terms of the quantity q produced and the
corresponding average and marginal cost functions.
Now, suppose that in the short-run, capital input is fixed so that = 100, and the wage
rate for is = $2 and rental rate for is = $2.
c) (3) Write down the short run cost minimization problem.
d) (5) Derive the short-run total cost function as a function of . Determine the firm’s
short-run variable cost and fixed cost.

4. Suppose there are 100 firms in a perfectly competitive industry. Each firm has a Ushaped,
long-run average cost curve that reaches a minimum of $10 at an output level of
8 units. Marginal costs are given by:
( ) = + 2
And market demand is given by:
= 100 − 20
a) (10) Find the long-run equilibrium in this market and determine the consumer and
producer surplus (in this case, the areas of the triangles)
b) (20) Suppose instead there was a single supplier whose marginal cost curve is:
( ) =
1
100 + 2
i) From the above expression for market demand, determine the monopolist’s
average revenue curve.
ii) From part (i), find the monopolist’s total revenue curve.
iii) If the monopolist’s marginal revenue is ( ) = 50 −

10
, what is its
optimal supply?
iv) Explain why this outcome is inefficient in comparison to the perfect
competitive outcome.

5. Consider a Cournot duopoly with the inverse demand = 200 − 2 . Firm 1 and 2
compete by simultaneously choosing their quantities. Both firms have constant marginal
and average cost = = 20.
a) (6) Find each firm’s best response function. Plot the best response functions (label the
x-axes as 1 and y-axes as 2
.
b) (6) Find the Cournot-Nash equilibrium quantities, profits and market price. Illustrate
the equilibrium point on your graph in part (a).
c) (5) Suppose instead that firm 1 had = = 20, but firm 2’s = 0. How
would this affect your answers to part (b)?

6. Consider an inverse market demand = 150 − 7 . Suppose there two firms in the
market, firm 1 and 2 have constant marginal and average cost = = 10.
a) (10) Suppose that firm 1 is a Stackelberg leader, i.e., it determines its output before
firm 2. Determine the Stackelberg equilibrium outputs and profits.
b) (20) Next, suppose there are 3 firms in the market with = = 10. Assume that
firm 2 and 3 continue to behave as Cournot (Nash) competitors, choosing their
outputs simultaneously. However, firm 1 remains a Stackelberg leader. Determine the
equilibrium outputs and profits of the three firms in this case. Contrast your answer to
part (a).