High Canadian Dollar Damaging to Exporters. An (Unexpectedly) Rising One Moreso

This is a post I've been meaning to write for months, but I couldn't find the words to do so.  Instead I've decided to create a very simple microeconomic model to illustrate my basic point - that since prices are sticky, an unexpectedly rising Canadian dollar can do more damage to an exporter's bottom line than a high but stable Canadian dollar.

The basic model is as follows: A Canadian firm produces in Canada and pays expenses in Canadian dollars, but sells to the United States in U.S. dollars.  The firm sets their U.S. dollar price based on what they expect the exchange rate will be during the period.  However, the exchange rate can differ from that expectation.  For some reason, the firm cannot hedge against this fluctuation (perhaps they are too small and hedging transaction costs are too high).

Variables of the model as follows:

• p - The price of the good in U.S. dollars.
• L - the value of the Canadian dollar (a.k.a. the loonie).  We will refer to the expected value of the Canadian dollar as E[L] and the realized version of the Canadian dollar as A[L].
• q - The quantity of the good sold.  We'll assume the firm has a downward sloping demand curve given by q = 1.2 - p.
• c - Marginal cost of production.  We will assume c = 1.  We will leave out any fixed costs.
• PR - Profit of the firm.  We'll call the expected profit (based on the expected exchange rate) E[PR] and the actual (or realized) profit A[PR].

The expected profit for the firm is E[PR] = p/E[L]*q - c*q, which simplifies to E[PR] = (1.2 - p)*(p/E[L] - 1).  The actual profit is  A[PR] = (1.2 - p)*(p/A[L] - 1).

Differentiate E[PR] w.r.t. p to find the optimal price to charge, which ends up being p* = 0.6 + 0.5*E[L].  We can substitute this into our equation for actual profit to find the profit the firm will make each period is given by:

A[PR] = (0.6 - 0.5*E[L])*((0.6 + 0.5*E[L])/A[L] - 1).

First, we'll examine the profit of the firm for the period at different values of the Canadian dollar when the value of the dollar is accurately predicted.

Given that 100% of the firm's revenues are in U.S. dollars and 100% of the firm's costs are in Canadian dollars, it is not surprising to see the firm experience lower profits when the Canadian dollar is higher. (Note - I multiplied the profit figure by 1 million, to make the numbers look more reasonable)  The firm responds to a higher Canadian dollar by raising the U.S. price of their goods, which naturally causing a decline in sales.

Next consider the situation where the firm guesses wrong about the value of the Canadian dollar.  They believe the dollar will be at parity, but the actual value of deviates from that:

When the loonie unexpectedly goes above parity, the firm ends up undercharging U.S. clients and receives suboptimal profits.  Note that the firm makes a higher profit when the loonie is at an expected $1.13 than when the loonie is at $1.09 and the firm expected it to be at $1.00. (Note: There's nothing special about these particular numbers - had I chosen a different demand function and cost structure, the numbers would have come out differently.  However, an accurate prediction of the loonie will always yield higher profits than inaccurate one).

One 'solution' to this problem would be to assume that the loonie is going to rise - in other words, consistently over-estimate the value of the Canadian dollar.  But if you do this, you will end up overcharging your customers and face reduced profits - as shown by the case where the loonie is both expected to be and ends up being at 96 cents vs. the case where the loonie is expected to be $1.00 but ends up being 96 cents.

Naturally the value of the loonie matters - in our ridiculously oversimplified model the profit of the firm is 10 times higher when the loonie is at $1.00 than when it is at $1.13.  But as we see, the problem is compounded when the rise is unexpected.

Comments

[Nick Rowe]

If the decision you would take depends on the information you receive, then that information has positive value. But if your decision would be the same regardless of what the information tells you, then the information is of zero value.

Someone proved that somewhere, but I can't remember who. (It's someone's theorem). Your example is an application of that theorem to exchange rate uncertainty. If you had information on what the exchange rate would be, you would set the price conditional on that information.

Hedging does not, in your example, eliminate the costs of exchange rate uncertainty. I think I'm right in saying that, if your firm is risk neutral, the opportunity to hedge is of zero value. So when you assume no hedging, you can make that assumption with no loss of generality. The firm will have no benefit from hedging.

[K]

Nick: I don't agree. They may be risk neutral, but the payoff may be highly concave. I.e. If they fail to pay their employees because they didn't hedge a collapse of the US dollar, they go broke.

Mike: The firm has a standard portfolio allocation (or asset/liability management) problem. But I don't see why they'd be doing fx prediction any more than any other random person. If they were good at prediction they should be running a hedge fund - but there is no reason why it should be mixed up with an export business.

[curtis johnson]

The firm must have a strategic plan in order to have immediate solutions to these problems. And in addition, with the high value of US dollars that has been the bases of other worldwide currencies, these is indeed a downfall to other firms. This can lead to bankruptcy like what you have written.