# Production Function In Medieval Europe Essay

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 =

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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

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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