Suppose an economy is producing $e^k$ amount of output per capita if it uses $k$ amount of capital per capita.

As the production function is strictly convex I am thinking the only steady state is at $k=0$; hence the answer should be that 'this model may not have a steady state equilibrium'.

Can someone please let me know if my thinking is correct?


1 Answer 1


You only provide partial information. E.g., this production function is unusual; is anything else unusual? Is depreciation still linear in $k$? Is the rate of population growth constant? etc.

If nothing else is unusual: you can repeat the usual steps for finding a steady state, find if a $k$ exists for which per capita savings/investment equal per capita depreciation: $$ s \cdot e^k = \delta \cdot k \tag{1} $$ Note that $k = 0$ does not work as you have $$s \cdot e^0 = s \neq 0 = \delta \cdot 0.$$

Note that convexity only guarantees that any interior equilibrium you may find would be unstable; increasing (decreasing) $k$ will increase (decrease) the LHS of (1) more than the RHS of (1), thus a positive (negative) shock will be further reinforced by increased (decreased) $k$ levels.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.