This Forbes article strikes me as a little dishonest; the argument made is that if only McDonald's workers were required to make $15 an hour, the prices wouldn't change, on the theory that as a capitalist they are already pricing at the optimum to maximize profits and market share. This is true, though their reduction of profit might make them choose another line of business. However, even the author admits that it would make a big difference if all of its competitors also had a raise in workers pay; then a natural increase to a new equilibrium price would result. As he states in the comments section:
It does indeed matter whether the pay raise is at Maccy D only or across the board. If its only at McDonalds then its as above. They cant raise their prices because no one else is and thus prices dont rise.
If all wages move to $15 an hour then there will be some mixture of job losses (ie, more automation) and price rises.
But the original question was, what happens to Big Mac prices of McDonalds pays $15 an hour: which is the question Ive answered.
The problem is that the Forbes article is applying a perfect competition micromodel to a price-leader oligopoly industry. Apparently I was in the last generation that taught monopoly and oligopoly theory in micro.
McDonald's is the price leader in fast food burgers so it would look at the market as if it were a monopoly, the price point it chooses would be followed by the rest of the industry (or at least that portion that wanted to stay in business or keep profit margins). In the fast food industry labor costs behave in the short run much more like fixed costs than variable costs, so increases in labor cost don't translate into much change in marginal costs, leaving the price point much the same. Of course the average cost increases, profit decreases, and level of production stays about the same.
The real impact on a firm like McDonald's comes from two other mechanisms. First, workers who make more tend to spend more, and if the wage increase is economy wide, that could be significant depending on the income-elasticity of demand for burgers (yes children, elasticity of demand can be for something other than prices!). My guess is that income elasticity of demand for fast food among minimum wage workers is pretty high. So at any given price, quantity demanded will be higher. I think it's fair to say that price-elasticity of demand in fast food is pretty high, so the marginal revenue curve is pretty steep. In a monopoly/price-leader oligopoly model it's probably discontinuous, so price changes very little as quantity goes up.
Since the American economy is dominated by this kind of industry (price-leader oligopoly) the results will be pretty much the same for any cost increase where fixed costs are high. The price and output effects really depend on the income-elasticity of demand.
Let me make a side note here to defend my comment that fast food industry labor costs behave like fixed costs rather than variable costs in the short run. Food service costs are dominated by the costs of meeting peak period demand each market day. It drives the size of the kitchen, seating area, and parking lot as well as the staffing. You measure efficiency in wait times. In off-peak periods, staff get breaks, go home because they have split shifts, or roll silverware. The industry might be labor intensive overall, but at the start of each shift you have to go with the staff you scheduled. Therefore the wage bill for that staff is a sunk cost; either the kitchen is open or it isn't; regardless if it is raining and no customers show up or if the coupon in the paper really works. In other labor intensive industries like construction, labor does act like a variable cost. A framing carpenter shows up and ill do about the same amount of work the first hour as they do the last hour. Tomorrow they start where they left off today. You can't look at the wage bill and treat it automatically as a variable expense.
The second mechanism is substitution for labor. Theoretically this could be a major factor, but I just don't see it. Substitute for labor with what? And if there is a good substitute, don't you think these large firms would have availed themselves of it anyway? I they could use less labor by better training or work organization, they don't need an increase in wages to prompt them to make such changes.
A couple of comments in closing. The literature for the last 50 years has been unable to make any convincing argument that a higher minimum wage results in less employment and bunches of think tanks have thrown billions of dollars into the effort to produce such a result. It's a damnable lie. Not even a myth. Drive a stake in it's heart; it's been dead a really long time. In fact anyone who opines that minimum wage increases drive unemployment has just proven they have read nothing about labor economics (or get paid a lot of money to ignore what they know to be true if they are economists).
Second, the average wage in the USA is about $24 an hour. It's half that in the hotel and restaurant industry. The minimum wage is $7.25 an hour and as low as $2.15 for tipped employees. I it had kept up with inflation since 1969 it would be a bit over $10 an hour. There is some pretty good economic evidence that the failure of the minimum wage to keep up with inflation is a major cause (probably THE major cause) of both poverty and increasing income inequality over the last forty years.