Extending the Learning-By-Exporting Hypothesis: Introducing a Credit Constraint

Abstract

This paper develops a theoretical framework which can be used to examine policy implications from the learning-by-exporting hypothesis. This work builds on previous theoretical literature by introducing a credit constraint. When credit is available, the analysis suggests that supporting a learning sector via an export subsidy is not necessarily advised to improve social welfare. The learning sector’s goods may be over-produced (relative to another non-tradable sector goods) when consumers can borrow freely for their consumption. If the learning sector’s goods are over-produced, social welfare will be improved via a tax on production.

Appendix

This appendix formulates our analysis under the traditional approach, where two tradable sectors exist without the access to financial markets.⁴ This modification does not affect the supply-side argument presented in this paper. The relative domestic price p ^d is still equal to Eq. 3. However, the demand-side argument needs to be modified by replacing a budget constraint 5 with a balanced trade condition:

$$\left( {Y_S - C_S } \right) + \bar p^w \left( {Y_M - C_M } \right) = 0.$$

Denoting X _M = Y _M − C _M , a modified social planner’s problem gives the following current-value Hamiltonian:

$$\begin{aligned} U\left( {C_M ,C_S } \right) + \tilde \lambda \left[ {B\left( {Q_H } \right)\left\{ {F\left( {\left( {1 - \alpha } \right)K_M ,\left( {1 - \alpha } \right)L_M } \right) + H\left( {\alpha K_M ,\alpha L_M } \right)} \right\} + X_M - C_M } \right] \\ \quad \quad \quad \quad + \tilde \mu \left[ {E\left( {Q_H } \right)G\left( {\bar K - K_M ,1 - L_M } \right) - \bar p^w X_M - C_S } \right] + \tilde \gamma \left[ {B\left( {Q_H } \right)H\left( {\alpha K_M ,\alpha L_M } \right) - \delta Q_H } \right] \\ \end{aligned} $$

The first-order conditions with respect to C _M , C _A , X _M , K _M , L _M give

$$U_M = \tilde \lambda ,$$

(10)

$$U_A = \tilde \mu ,$$

(11)

$$\bar p^w = \frac{{\tilde \lambda }}{{\tilde \mu }},$$

(12)

$$\frac{{\tilde \lambda }}{{\tilde \mu }} + \frac{{\tilde \gamma }}{{\tilde \mu }}\phi = \frac{{E\left( {Q_H } \right)G_j }}{{B\left( {Q_H } \right)\left[ {\left( {1 - \alpha } \right)F_j + \alpha H_j } \right]}}\;{\text{for}}\;j = K,L$$

(13)

Equation 12, (together with Eqs. 10 and 11), indicates that the marginal rate of substitution is equal to the world relative price (i.e., the world’s terms of trade).

Equation 13, the domestic marginal rate of transformation, suggests subsidizing the learning manufacturing sector. Using Eqs. 3, 12 and 13, we have the following relationship between p ^d and $\bar p^w$:

$$p^d \equiv \frac{{\tilde \lambda }}{{\tilde \mu }} + \frac{{\tilde \gamma }}{{\tilde \mu }}\phi \geqslant \frac{{\tilde \lambda }}{{\tilde \mu }} = \bar p^w ,\quad 0 \leqslant \phi \leqslant 1.$$

(14)

The domestic relative price of manufacturing goods is greater than the world relative price. Firms produce based on the domestic relative price (or the marginal rate of transformation), which is greater than the world relative price (or the marginal rate of substitution in consumption). This implies that a learning manufacturing sector produces less than socially optimal output. Social welfare improves if the government subsidies close the gap between p ^d and $\bar p^w$.