Posted: October 9th, 2017
. (8 points) Consider 100 firms that each have a Cobb-Douglas production function of
Q = B.2 K.2 L.3 in which capital and labor are both flexible in the short-run and the longrun
and buildings (B) is fixed in both the short-run and the long-run at 1 unit. Each firm
w = 10, r=20, PB = 10346
The demand curve in this market is
Q = (4,350,340.426)/P
a) What are the equilibrium price, equilibrium quantity, quantity offered by each firm,
and profits of each firm in the short-run?
b) What are the equilibrium price, equilibrium quantity, quantity offered by each firm,
and profits of each firm in the long-run?
2. (7 points) Consider a country that uses only labor in production of Good X and Good
Y. The production functions of Good X and Good Y are:
X = 2 LX
Y = 10 LY
The country has 100 workers that can be allocated between the two sectors. Note: This
means that LX = 100 – LY
a) Draw the Production Possibilities Frontier of this country. What is the equation for
the slope of the Production Possibilities Frontier in terms of X and Y?
b) Without trade with the rest of the world, how much of Good X and Good Y would this
country produce and consume. What would the ratio of price of Good X to price of Good
c) If the rest of the world is willing to trade with this country at a price of 1Y for 1X.
How much would this country produce and consume of each good? How much better off
is the country with trade than without trade?
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