intermediate microeconomics
show your work and illustrate your answer with appropriately labeled diagrams
u) Calculate the incumbent as pro t mnxtmmng output and pmf:tL
b) St apoltmlalcntnnt (L) la :.umcmpLlnmag cmry mm the manta. mt does. It
r (I
lhcumcoperltlllgconl. but must lnwustsit-t:p(l’tud)t:4M. bmccthccmsflasaulyun L
mukegiustau-upcomtsuo Ml mustbctncludcdmthcpml’ncaIcdnna;SflP°”‘=
the eon la 825 (which makes its cost TC‘ 825 + I
I. Suppose the incumbent behaves as I btackclberg leader (mad the ennui amid
obviously be the follower). Calculate the profit of both linm
V 4
ii If W incumbent would belut ‘ ‘ than his
L vcslratcgtutllyandproduccwtnnumoac
(Suckelbet-3 Iader 5 output. calculate the profit 0! both fimu.
c) Using your answers in put 3:) and 3b) above, wmstruct a gun: me.
id U ’ 3 nbov clctcrm‘
your answer tn part ~c) e. me the Nash eqmlabnmt
e) Suppose the nun-up mt In 725 instead of 825, ather thing: being equal. construct the gun:
nu. (Him. you need to redo pan 3b) wtth new cost functton for the entrant).
Gi l 3 tbov” determ‘ the ash
venyouruuwer apart e) L e, tncL N eqmltbrmn.
Show your work and illustrate your answer with appropriately labeled diagrams.
1, A monopolist sells its product in two different markets. The demand curves in these markets are:
P; 200 -~ 0.50) and P3 = 250 – l.5Q2. The firm produces the output in one facility. the cost curve
ofwhich is given as: TC = o.5Q“ – 5Q (which implies MC = Q + 5).
1) Suppose the firm sells 100 units in total. Using graph (grid) paper. determine the quantity it
must sell in each market for maximizing TR. Calculate the TR for Q = 100. Is Q ” 100 Pmfi‘
maximizing? Explain and illustrate your answer graphically.
b) Calculate the profit maximizing total output (Q) of the monopolist and the quantity sold in each
market. Calculate the profit. Illustrate your answer.
c) Do the profit maximizing prices in these markets satisfy the theoretical prediction about the
relationship between price and elasticity’? Explain.
(Hint: you need to calculate the elasticity at the equilibrium quantity in each market.)
2. Suppose that Panasonic, a Japanese firm, and Zenith, the U.S. firm, are the only two firms that can
potentially produce a new type of high-definition TV. The pay-offs (in million dollars) from
entering this product market are given in the pay-off matrix below:
Panasonic
Enter Do Not Enter
Up = – 40 Up = O
Zenith
Up = 250 Up = 0
Do Not Enter Up = 0 Up = 0
a) If both firms move simultaneously, does either firm have dominant strategy? Explain.
b) Is there a Nash equilibrium in this game? Is the equilibrium unique? Explain.
c) If the U.S. government commits to pay Zenith, the U.S. company, a subsidy of 50 if it enters
market, what would the Nash equilibrium? Explain your answer.
d) If Zenith does not receive the subsidy buthas a head-start over Panasonic, what would be the
Nash equilibrium? Explain axtswer.
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