Question

Imagine a country X that produces only two goods, strawberries (S) and cars (C), using two factors of production, capital (K) and labour (L). The production functions for both goods are given by :

Qs = Qs(Ks , Ls)

Qc = Qc(Kc , Lc)

Qs is the total strawberry output, and Qc is the total car output. K and L are capital and labour inputs, respectively. Since it is difficult to pick strawberries by machines, we assume that strawberry production is labour intensive while car production is capital intensive. In the production of both goods, capital can be substituted for labour and vice versa. Answer the following questions using the information provided above.

Suppose the total labour supply of country X has been negatively affected by the Covid-19 pandemic. In the absence of trade, and for a fixed relative price of strawberries to cars, ps divided by pc, what will happen to country X’s production decision with the fall in labour to capital ratio, L divided by K. [Hint: show with a graph the change in the outputs of strawberries and cars before and after the change in the labour to capital ratio]

Answer 1

Sol.

Two goods strawberry [S] and car [C] are being produced with labour and capital . Sis labour intensive and C is capital intensive .

In the figure strawberry is measured from lower left corner and car from upper right corner . Initial equilibrium is at H ,where Q_s0 of S and Q_c0 of C are being produced . Now labour supply falls to L₁ . To keep relative price of goods constant , factor intensity should be constant(assuming linearly homogeneous roduction function) . New point of production is G , at this point factor intensities in the two lines of production are same as on H because MG is parallel to O''H ,  G and H are on the same line. At G , production of S declines to Q_s1 and of C increases to Q_c1 . This conclusion is in accordance with Rybczynski Theorem . So production of labour intensive good strawberry falls and of capital intensive good car rises.

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