# Production Function In Medieval Europe Essay

1476 Words 6 Pages
Suppose the production function in medieval Europe is Y= K0.5L0.5, where K is the amount of the land and L is the amount of labor. The economy begins with 100 units of land and 100 units of labor.
Production function: Y= K0.5L0.5
K = Land = 100 units.
L= Labor = 100 units.

• How much output does the economy produce?

Y= K0.5L0.5
Y = 100^0.5 * 100^0.5
Y = 100
The output of the economy is 100 units.

• What are wage and rental price of the land?

ΔProfit = ΔRevenue − ΔCost = (P * MPL) − W.
P = Price level.
MPL = Marginal price of labor.
W = Wage

But in the perfectly competitive scenario, ΔProfit = 0 for all the firms.
So,
W = P*MPL
As P is not given, we will assume that the price level P =1

Real wage = W/P = MPL = dY/dL =
So MPL = Real Wage = 0.5.

Similarly,
Rental price of land = MPK = dY/dK = d(K0.5L0.5)/dK = 0.5* L0.5/K0.5
Here K = L = 100 units.
So MPK = Rental price of land = 0.5.

• What share of output does labor receive?

Cobb–Douglas production function.
F(K, L) = A (K)^a * (L)^(1-a) a: constant between zero and one that measures capital’s share of income. That is a determines what share of income goes to capital and what share goes to labor.
A: Parameter was greater than zero that measures the productivity of the available technology.
Converting the given function Y= K0.5L0.5 into the above form.
We get a = 0.5 and A =1.
Thus, 50% share of output does labor receive.

• If a plague kills half of the population, what is the new level of Output.

L’ = L/2 = 100/ 2 = 50

Y= K0.5L’0.5
Y = 100^0.5 * 50^0.5
Y = 70.71 units
The output of the economy is 70.71
That is a determines what share of income goes to capital and what share goes to labor.

A: Parameter was greater than zero that measures the productivity of the available technology.

a = 0.3
So, 30% output will go to land, and 70% of output will go to the labor.

L’ = 1.1L
Y= K0.3L0.7
Y’ = K0.3L’0.7 = K0.3 * 1.1 L 0.7 = 1.1 K0.3L0.7 = 1.1Y
So, output increases by 10%.

Rental price of capital
MPK = d(Y)/ dK = d(K0.3L0.7)/dK = 0.3 L0.7/ K0.7
MPK’ = 0.3 L’0.7/ K0.7 = (0.3*1.1) L0.7/ K0.7
MPK’ = 1.1MPK
The rental price of capital will increase by 10%.

Real wage = MPL
MPL = d(Y)/ dL = d(K0.3L0.7)/dL = 0.7 K0.3/ L0.3
MPL’ = d(Y)/ dL’ = d(K0.3L0.7)/dL’ = 0.7 K0.3/ (L0.3*1.1) = MPL/1.1
MPL’ = 0.91 MPL
The real wage decreased by 9%.

K’ = 1.1K
Y= K0.3L0.7
Y’ = K’0.3L0.7 = 1.1* K0.3L0.7 = 1.1Y
So, output increases by 10%.

Rental price of capital
MPK = d(Y)/ dK = d(K0.3L0.7)/dK = 0.3 L0.7/ K0.7
MPK’ = 0.3 L0.7/ K’0.7 = 0.3 L0.7/ K0.7 *1.1 = MPK / 1.1
MPK’ = 0.91MPK
The rental price of capital will decrease by 9%.

Real wage = MPL
MPL = d(Y)/ dL = d(K0.3L0.7)/dL = 0.7 K0.3/ L0.3
MPL’ = 0.7 K0.3/ L’0.3= (0.7 * 1.1) K0.3/ (L’0.3) = MPL*1.1
MPL’ = 1.1 MPL
The real wage will increase by

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