Question

ne is able to use Gin (G) and Vermouth (V) to produce martini. A regular martini is produced with 2 portions Gin for 1 portion Vermouth. A dry martini is produced with 5 portions Gin and 1 portion Vermouth. The prices of a regular martini (PM) and a dry martini (PD) are fixed. You have a given supply to both Gin (G) and Vermouth (V).

Derive the production possibility frontier of martini, with QM, the quantity of regular martini on the y-axis and QD, the quantity of regular martini on the x-axis. For what range of prices you only produce/sell dry martini? a) Draw the relative supply curve using the relevant axes. Label your plot as thoroughly as possible.

Answer 1

The following numerical falls under Heckscher-Ohlin's theory of the International trade.

Let us make it clear first by an assumption,

1.We know study a model of trade where all factors of production are
flexible in the long run.
2. The technologies used to produce different goods will use different factors relatively more intensively.
3. With more than one factor and differences in production technologies
across sectors (different relative factor intensities), differences in
factor abundance are enough to generate differences in country PPFs
and relative supply curves –and hence a pattern of comparative
advantage

The technologies for producing C and F are represented by the
production functions QC = FC (KC , LC ) and QF = FF (KF , LF )
The production of C is labor intensive relative to the production of F
(which is capital intensive relative to C)
Both labor and capital can move across sectors
... and hence must be paid same factor prices in both sectors (if both
goods are produced)
Subject to endowment constraints L = LC + LF , K = KC + KF
Like in the specific factor model, for any labor allocation LC , LF ,
there is a relative price pC /pF s.t. pCMPLC = pFMPLF (labor
allocation is efficient)
... but arbitrary capital allocations KC , KF will, in general, not be
efficient at these prices: pCMPKC = pF MPKF
... we need to determine jointly the efficient allocation of capital and
labor, as well as the factor prices that sustain that allocation

Unit input req. determine factor
allocations and production
LC + LF = L QC aLC + QF aLF = L
⇔ KC + KF = K QC aKC + QF aKF = K

Given (aLC , aLF , aKC , aKF ), this can be solved for (QC , QF ) and hence
(LC , LF ,KC ,KF )

Numerical: