Thursday, April 02, 2009

Listeners Are Smart, So A PD Has To Be Smarter (Or Try To Be)

Reid Morgan, PD for Jim Pattison's Country 95/B93 combo in Lethbridge writes: We are airing some "buy local" spots and one of them talks about the "multiplier effect" with the formula number being 8.

So, a U of L economics professor contacts me and wants to know how we came up with the number 8. They were actually working on it in one of her classes trying to figure out our formula. (Imagine a university class discussing/debating a radio ad on Country 95, nice) I emailed what I could find and here is her response. (both below)

Dear XXX, The marginal propensity to consume (MPC) is equal to ΔC / ΔY, where ΔC is change in consumption, and ΔY is change in income. If consumption increases by eighty cents for each additional dollar of income, then MPC is equal to 0.8 / 1 = 0.8.

The expenditure multiplier is the ratio of the change in total output induced by an autonomous expenditure change.

 -- Reid Morgan, CRM
Director of Programming

2. Thank you so much so sending this to me Reid. Now here we go….this is in fact Keynesian ‘s model, HOWEVER, this is his simple model with very strict assumptions that does not exist in the real world.

First, this is assuming we live in a world that has NO taxes, now that would be nice, no income tax, no property taxes, no excise tax i.e. gas, alcohol or cigarette taxes, no sales tax and NO GST. The Consumption function looks like this C = Co + mpc(Y –T), where Co is the amount of consumer spending you do that does NOT depend on your income, mpc you have correct, but you are multiplying it by Y which is national income, not after tax income.

Yd = Y – T, which is consumer household after tax disposable income. T = stands for total tax revenue, that takes into account all taxes collected by the government, a simple version of this is T = T0 + tY, where t is the propitiate income tax Canadian’s pay, and T0 is all other taxes., again this is over simplified.

Therefore, C = C0 + mpc{Y –(T0 + tY)} = C0 –mpcT0 + {mpc(1-t)}Y

Second, Canadians buy imported goods on a daily basis, consider a banana, that is an imported good, and goes not increase Canada’s GDP(Income), therefore you must take this into account for the multiplier.

Now NX = X – IM = X – {IM0 + mpi(Y-T)}, note that household spend money on imported goods such as bananas that does not depend on their income, that is IM0, but there the rest of the imported goods does depend on your after tax income, such as a trip to the US.

Therefore, if you take into account we do pay taxes and buy imported goods the Multiplier = 1/{(mpc-mpi)*(1-t)}

If you run the numbers through it will be LESS THAN 5.

Now, I have simplified the real word case, but in actuality, the BANK OF CANADA calculates the Canadian Multiplier using approx. 1000 formulas that takes into account almost everything and when doing so the Bank of Canada calculates an expenditure multiplier between 1 and 2, but closer to 1.

Finally, if we just have the average household in Lethbridge spend $20.00, this will not have an effect of 5 times. We must realize that we spend AFTER TAX income, and we have to pay GST on goods, and if we spend it on gas, we pay an excise tax to the government. Second the individual may be buying imported goods not Canadian goods.

Therefore, spending $20.00 locally will not generate what your (public service ad) has suggested. This is a one time spending, this will not see a permanent increase in the Canada’s GDP. Rather you are taking your after tax income to spend on goods that already exist in the economy, it will be a one day blip, that will not realize an ECONOMIC BOOST! Households must continue to spend and increase spending to see any effects in the positive direction.

If you have any questions, or would you like to chat, by all means give me a call or e-mail. I would be happy to discuss this issue.

In forwarding the interchange along, Reid added: "I'm glad I'm in radio and the toughest math I have to do is figuring out song rotations or my Can. Con. numbers. ; >"

All I can add to THAT is: in this economy, we're all being forced to learn more economics than we ever thought we would need to.


Dan said...

I remember getting ripped on in radio when presenting corrected math to those in charge of calculation.....truth is not beauty.... creative teams may have more fun enforcing a comfortable local dependable neighbour image for clients than an overt call to action to consume....check the bottom line in eight weeks and correct me... ;)

Crystal Darche said...

Ow, my brain hurts after reading that! - Crystal Darche, JRfm Vancouver