Question

The specific factors model

View Zoom Add Slide Table Chart TextShape Media Comment Share Tips Format Animate Document Slide Layout Change Master The specific factors model Title Body Slide Number The allocation of labor between sectors Color Fil FX MPL (Labor demand in the food sector) Edit Master Slide PM X MPLM Labor demand in the 19 Labor employed in the manufacturing sector,LM Labor employed in the food sector , LF Overall labor supplyL Slide 3-18

1) Consider a family of farmers. Grandma owns the machinery necessary to produce corn, while Grandpa owns the machinery necessary to produce soybeans. Their children carry out the work required to produce both corn and soybeans. Assume that production functions for the two goods are concave in labor.

(a) Starting with the profit maximizing condition w = P × M P L, derive the diagram we have introduced in class. In the diagram, show the areas representing total wages and Grandma and Grandpa’s income.

(b) Assume now that the relative price of the two goods changes and assume also that the price of soybeans increases. How will this affect the income of the members of the family?

2) Consider again the specific factors model and assume that we are in Australia. In your opinion, which migration policy will be favored by the landowners in that country? Which one will be favored by the owners of manufacturing plants? Discuss your analysis using the diagram we have introduced in class.

Answer 1

1)

a) According to the profit maximizing condition, W = P x MPL , we derive two labor demand curves specific to two goods being produced here.

The corn marginal revenue labor product curve is represented by P_c x MPL_c is sloping downwards with labor increasing in corn sector from left to right. The soyabean marginal revenue labor product curve P_s x MPL_s is moving downwards with labor increasing moving from right to left.

The will equate at the point where wage rate in both the sector equalise and hence labor will be distributed accordingly to both sectors.

b)

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Assuming relative prices change due to rise in price of soyabean, then such a change will shift the Marginal revenue product curve for soyabean upwards, thus creating a new equlibrium point with a higher wage in soyabean sector causing labor to move to soyabean sector for higher wage.

Such change in price will raise the income of Grandpa as his income will rise due to rise in price. Grandma's income will reduce as due to rise in wages , labor is now more costly to her in real terms.

2) Taking the above diagram as reference point. Labor will move to that sector which offers higher wage rate and a sector will offer higher wage rate only if its relative price rises. So if a sector in which land is a specific sector and the price of that good rises then landowners will be better off ( as shown in diagram above where a rise in price in soyabean improves Grandpa's income as marginal revenue labor product moves up) so landowner would prefer migration policy which turns labor to the sector with land as specific factor. Similarly owners of manufacturing plant will prefer such policy which will induce labor to move to sector specific to their factor.