Question

One 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). what are the prices of Gin and Vermouth, i.e. WG and WV? You can think of these prices as analogs of the wages for labor and rental rate for capital. Hint WG and WV should be expressed as equations written in terms of PM and PD.

a) Using the previous part, answer the following question: Suppose that the price of dry gin PD increases. Does this increase change wg and wv? If you did not solve the previous part of the problem, explain intuitively what should happen to wg and w.

Answer 1

Given: Let the quantity of gin required per portion be G and Vermouth be V, then

Regular martini requires: Gr = 2 and Vr = 1

Dry Martini requires: Gd = 5 and Vd = 1

Price of regular martini = Marginal revenue (MRr) = PM

Price of Dry Martini = Marginal Revenue (MRd) = PD

Marginal cost of Regular martini = MCr = Gr *WG+ Vr *WV = 2WG + 1WV = 2WG + WV

At equilibrium: MRr = MCr

PM = 2WG + WV.................. (1)

Marginal cost of Dry martini = MCd = Gd *WG+ Vd *WV = 5WG + 1WV = 5WG + WV

At equilibrium: MRd = MCd

PD = 5WG + WV ..................(2)

Solving equation (1) and (2), we get,

PM = 2WG + PD -5WG

=> 3Wg = PD -PM

or, WG = (PD -PM)/3

WV = PD - 5WG = PD - 5[(PD -PM)/3] = (3PD - 5PD +5PM)/3 = (5PM - 2PD)/3

=> WV = (5PM - 2PD)/3

Now, if price of dry gin increases, WG will increase while WV will fall as can be seen from the equation that dWG/dPD is positive while dWV/dPD is negative.

This result is explained by the Stopler-Samuelson Theorem of international trade that describes the relationship between relative prices of output (PD and PM) and relative factor rewards (WG and WV).