NRU HSE-2015, Microeconomics
Due on November 16, 2015
Monopoly/monopsony and price discrimination
Reading: Pindyck Robert S., Daniel L. Rubinfeld, Microeconomics, 8th Edition, Pearson Series in Economics, 2013, Ch. 10
and Ch.11 (sections 11.1-11.2 and 11.4) and Appendix to Ch.11
TOTAL SUM is 11 (i.e. bonus=1)
1. (1 p.) Question is based on Figure 11.5 ‘Third degree price discrimination’ (p.407 P&R). This figure represents graphical
derivation of equilibrium under third-degree price discrimination when monopolist has increasing marginal cost. Read the
following comment to Figure.11.5: “the total quantity produced, QT  Q1  Q2 , is found by summing the marginal revenue
curves MR1 and MR2 horizontally, which yields the dashed curve MRT , and finding its intersection with the marginal cost
curve”.
As we know the first order conditions suggest that marginal revenue for each group separately, not the total marginal revenue
should be equal to marginal cost. Is there a contradiction? What equation do you solve by constructing this MRT ? Explain
your answers.
No contradiction. Explanation (0.5) Equation with comments. (0.5)
2. (4 p.) A monopolist has two customers with the following demand functions:
Q1  10  p and Q2  12  p . The
monopolist’s cost function is TC Q   0.25Q .
(a) Suppose that monopolist can differentiate between the customers and offers two part tariffs. Find the optimal two part
tariffs. Provide both analytical and graphical solutions.
Linear price (0.25), Fee (0.25 per each group) Graph. (0.5)
(b) Now suppose that monopolist cannot discriminate between the groups. Find the optimal two part tariff.
Profit if monopolist deals with high valuation group (group 2) only (0.5)
Optimal tariff if monopolist deals with both groups. (0.5)
Calculation of profit, comparison and conclusion. (0.5)
(c) Calculate the value of society loss in (a) and (b), Compare and explain the result.
DWL a (0.25) DWL b + comparison (0.5) Explanation (0.5)
2
3. (6 p.) In town N only one firm offers job to engineers. The inverse labour supply curve by female engineers is given by
LF w F  max 0, w F  4 and inverse labour supply curve of male engineers is LM w M  w M , where w k stays for
wage rate of group k ( k  M , F ). Assume that labour is the only variable factor in the short run and the short run production
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function of the firm is F L   max0, 13L  0.5L2  . The final product is sold at perfectly competitive market and the price
is $4 per unit.
(a) Find the profit maximizing wage rates assuming that the firm can set different wage rates to male and female engineers.
Illustrate by graph.
Calculation of profit maximizing wage rates (0.75) Graph (0.75)
(b) Now assume that price discrimination is not allowed any more. Find equilibrium. Illustrate graphically on the same graph
with different colour.
Equilibrium (0.75 p.) Graph. (1 p.)
(c) Compare social welfare in (a) and (b) by calculating the difference in the total surplus? Provide intuitive explanation
(explain carefully).
Comparison of social welfare (0,5 p.) Explanation. (1 p.)
(d) Suggest taxes\subsidies which can be used to induce the discriminating monopsony from part (a) to choose efficient
employment. Demonstrate that proposed solutions would result in efficient outcome.
Comments on the choice of instruments (two subsidies). (0.25 p) Efficient employment (0.5 p) Calculation of the subsidy rates
(0.25 p. each)