Corn Whiskey country

The economy is populated with L people. All the people are consumers and producers at

the same time.

Let x be corn and y be whiskey.

As consumers all people buy corn and whiskey from the market for consumption. Their

utility function is u = x · y, so each and every one of them spends half of their income on

coke and the other half on whiskey. As producers, each of them is endowed with 1 unit of

labor and have access to two production technologies:

• A person can use one unit of labor to grow αx units of corn

• A person can use one unit of labor and 18 units of corn to make αy units of whiskey

They can freely choose to use any of these technologies.

Let us denote Lx the number of people who chose to produce x (corn) and Ly the number

of people who chose to produce y (whiskey).

3

(a) (3 points) Write down the equation that should be true for αx, αy, px, py in equilibrium.

Explain why this equation is true.

(b) (1 point) Write down the expressions for the supply of corn (Xs) and whiskey (Ys).

(these should be algebraic expressions involving αx, αy, Lx, Ly)

(c) (3 points) Let I be the equilibrium GDP in this economy. Write down the expressions

for the demand for corn (Xd) and whiskey (Yd) (these should be algebraic expressions

involving I, px, py, Ly). (Hint: corn is demanded both for final consumption and as an

intermediate good for production of whiskey)

(d) (2 point)Write down the expressions for I (this should be an algebraic expression

involving αx, αy, px, py, , Lx, Ly).

(e) (3 points) Let L = 360, αx = 42, αy = 0.5. Together with the resource constraint

(Lx + Ly = L), normalization (px = 1) and market clearing (supply equals demand for

each good), solve the above equations for Lx,Ly and py. Show work.

(f) Write down

• (1 point) equilibrium quantity of whiskey, equilibrium quantity of final consumption

of corn, equilibrium quantity of intermediate consumption of corn

• (1 point) GDP,

• (1 point) value added of corn industry, value added of whiskey industry.

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Status NEW Posted 05 Jun 2017 07:06 AM My Price 12.00

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