Posted: October 9th, 2017

# 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?

. (8 points) Consider 100 firms that each have a Cobb-Douglas production function of

the form:

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

faces:

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

.5

Y = 10 LY

.5

The country has 100 workers that can be allocated between the two sectors. Note: This

means that LX = 100 – LY

The Societal Indifference Curves are Cobb-Douglass of the form: U = X.5 Y.5

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

Y be?

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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