Any movement of laborers from one sector to another would affect the wage, but this is not possible. As long as the wage is identical in both sectors, labor supply is perfectly inelastic with respect to wage. Recall that for a perfectly inelastic supply curve there is no excess burden. Labor must bear the entire tax burden, however. Consider the general capital tax.
Capital is supplied perfectly inelastically in both sectors.
The tax shifts the demand for capital downwards by the amount of the tax, lowering r. Again there is no excess burden. You should draw some of the relevant supply and demand graphs to understand fully what is going on here. Capital is immobile, so there is now too much labor in the food sector and too little in the manufacturing sector. In the manufacturing sector the price of capital fell while the price of labor increased.