General Equilibrium Elasticities

Derivation and Interpretation

One of the big problems in general equilibrium analysis stems from the fact that firms do not face a single demand schedule, from which we can read off the demand elasticity for a given product. Rather, the typical firm/industry sells to many different agents in the economy. Some of these are domestic firms, some are domestic households and some consist of overseas buyers of exported goods. Thus the demand elasticity faced by a sector in the GTAP model is a composite of many different agents responses to a price change. This is still manageable analytically, in the sense that the market demand elasticity can be computed as a share-weighted average of the individual agents responses. For example, if 10% of steel output is sold to the domestic automobile industry and that industrys conditional, own-price elasticity of demand for steel is 0.10, then the contribution of the auto industry to steels total, partial equilibrium demand elasticity would be 0.10 * 0.10 = 0.01.

However, in general equilibrium, automobile firms response to an increase in the price of steel will be more complicated. In particular, this will tend to force the price of automobiles up. As a result, the total number of autos sold is expected to decline. This output effect must be added to the substitution effect captured by the conditional price elasticity of demand to get the total effect. However, the story does not stop there. Because the increase in the price of steel raises the price of other products, some of which may themselves be substitutes for steel, one must also take into account cross-price effects. Finally, income in the economy may be affected, in which case income effects will also come into play. The only way to capture all of these components of the general equilibrium demand elasticity is via model simulation.

Simulation of the general equilibrium elasticities of demand proceeds as follows. The output tax on steel is perturbed by 1 percent. This in turn causes the market price of steel to rise by something less than 1 percent, say 0.6% (the remainder is borne by producers in the form of a decline in the agents supply price). We then observe the reduction in market demand, which might be 0.9%. In this case, the general equilibrium elasticity of demand for steel in the model would be -0.9%/0.6% = -1.5%. But how much of this is attributable to different agents? To answer this question, we need to observe the change in demand by all of the different agents in the model. Auto producers might show a reduction in steel demand of 0.08%. We then divide this by the market price change to find the auto sectors GE, own-price elasticity of demand for steel = -0.08%/0.6% = -.13. If we then multiply this elasticity by the auto sectors share of total steel demand we obtain their contribution to the total GE demand elasticity for steel = 0.1 * -0.13 = -0.013. For a small perturbation, the share-weighted agents responses will add up to the total GE demand elasticity.

Now read: Use of the GEELAST header array file

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