02 Jun Question Econ 101A — Midterm 2 Th 10 April 2014.
Question
Econ 101A — Midterm 2
Th 10 April 2014.
You have approximately 1 hour and 20 minutes to answer the questions in the midterm. We will collect
the exams at 11.00 sharp. Show your work, and good luck!
Problem 1. Monopoly with Fixed Cost.(55 points + extra credit). Consider the case of a
monopolist producing quantity?with total cost?(?) =?+???with? ?0and??0?
1. Comment briefly on the cost function. Does it involve a fixed cost? (5 points)
2. Determine the marginal cost function?0?and the average cost function?(?)???and plot the two
functions in a graph with x-axis quantity?and y-axis cost/price. (5 points)
3. Assume now that aggregate demand is given by the linear (inverse) demand function?(?) =?????
with? ? ??Draw it in the graph with the marginal cost function of point (2). If you want, assume
?= 10? ? = 5? ?= 1? ?= 1(just for the graph) Also, derive the marginal revenue??function, by
differentiating with respect to?the revenue??and draw the??=?0function in the graph. (5
points)
4. Find graphically the solution for monopoly quantity and price (5 points)
5. Still graphically, indicate the producer surplus or profits of the monopolist. Indicate which of the two
methods you are using. (5 points)
6. Now solve analytically for the monopoly solution, by maximizing
max
?
???(?)??(?) =?(????)??????
Obtain the first order conditions and solve for??and???the monopoly solution. (5 points)
7. Compute now the profits analytically, plugging in??and??in the solution above. (5 points)
8. A consultant to the government claims, regarding this monopoly: ‘A big problem with monopoly in
this industry is that profits are unfairly high’. Is that always true? Can you give conditions under
which monopoly profits in this case would bezero? (10 points)
9. Continuing on the point above, can you give conditions under which monopoly would havenegative
profits? Going back to the figure, what would the average cost curve look like in that case? What
would the monopolist do in that case? (5 points)
10. Given the above point (9), revise the solution at point (6) for the optimal monopoly solution. (5 points)
11. (Extra credit, do not attempt till you have done Problem 2) If we were in perfect competition, and
each firm had the same cost curve as above, and faced the same demand curve is as above, what would
be the supply function and what would be the perfect competition equilibrium, if any? Why? (15
points)
1
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