11.05.2023 Specific Factor Model#

Model that allows income to be a part

Assumptions#

  • two goods: cloth and food

  • tree factors of production: L, K, T (land)

  • perfect competition

Definition#

  • Cloth Inputs: Capital + Labor (not Land)

  • Food Inputs: Land + Labor

  • Labor = mobile factor

\[\begin{split} Q_C = Q_C(K,L_C) \\ Q_F = Q_F(T, L_F) \end{split}\]

  • more people employed in one production = more output

  • but diminishing returns

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Marginal Product of Labor:

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Production Possibilites#

  • Labor split between Sectors

  • \(L = L_C+L_F\)

Four-Quadrant Diagram for PPF

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Quadrants:

  • lower left: Allocation of Labor

  • lower right: Production Cloth

  • upper left: Production Food

  • upper right: combinations of both

PPF sloped because of diminishing returns

opprtunity Costs of one more cloth

  • is \(\frac{MPL_F}{MPL_C}\) pounds of food

  • need \(\frac{1}{MPL_C}\) hours of labor

  • to free up one hour: reduce food by \(MPL_F\) units

  • Result:

    • \(MPL\) in Food rises (less workers there)

    • MPL in Cloth falls (more workers there = each less productive)

    • \(\frac{MPL_F}{MPL_C}\) rises

Labor Allocation#

How much labor in each sector?

Demand: where MPL of one hour = Marginal Cost of one hour $\( W = MPL_C \times P_C \\ W = MPL_F \times P_F \)$

  • two sectors must pay same wage (mobility)

  • Demand for Labor = \(MPL_C\) (second Figure) times \(P_C\)

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Wage = Equilibrium

Production#

at Production Point: PPF tangent to relative Prices $\( -\frac{MPL_F}{MPL_C} = - \frac{P_C}{P_F} \)$ 2023-05-11_13-11-16

Shocks#

Change in relative Prices (not equal in goods)

If \(P_C\) rises:

  • labor shifts to Cloth Sector

  • Output of Cloth Sector rises

  • w rise not equal to rise in prices

    • Employment Increase = MPL falls

    • higher cost of employment

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Economic Effect:

  • Capital owners = profits rise

  • Land owners = less profits

  • Workers = depends

    • relative preference of cloth and food

International Trade#

Price determined by Relative Supply / Demand

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Opening up:

  • if RS in economy > RS in world economy

  • => price increase

Gains from Trade:

  • allows mix of consumption

  • different from production

  • but spending = income from production

\[ P_C D_C + P_F D_F = P_C Q_C + P_F Q_F \]

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  • Economy as whole profits

  • Budget Constraint above PPF

But:

  • profits the non-mobile factor (K / T) of export sector

  • mobile sector = ambiguos

    • produces losers and winners (consumers)

    • often hurts relatively poor workers (garment workers in DE)

=> Redistribution from winners to losers

Unemployment#

International Trade:

  • Shifts jobs from import-competing to export sector

  • temporary unemployment

but unemployment = mostly macroeconomic

Instruments:

  • extended unemployment benefits

  • skill acquisition financially supported

Exercise#

\(w = MPL * P\)

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Shift of Price 50% upward of Good 1

  • w in the Sector 1 rises

  • Red Line shifts upward because of Formula

  • wage rise not exactly 50% but less because of Markets