Tax Incidence
Statutory incidence (who writes the check to the government) rarely matches economic incidence (who bears the loss of surplus).
The Rule of Elasticity
The burden of a tax falls more heavily on the side of the market that is less elastic. If consumers cannot easily change behavior (inelastic demand), firms will pass the tax burden forward via higher prices.
Example: Payroll Taxes
While payroll taxes are often split 50/50 statutorily between employer and employee, empirical labor economics shows that labor supply is highly inelastic compared to labor demand. Therefore, workers bear almost the entirety of the payroll tax via depressed wages.