Question

If a price floor benefits producers, why does a price floor reduce social surplus?

Short answer

Consumer surplus lost is greater than the producer surplus gained.

Step-by-step solution

Step1. Introduction

Social surplus is the sum of consumer surplus and producer surplus.

Step 2. Explanation 

When a price floor is imposed, the producer surplus increases. But this price floor causes consumer surplus to decrease. Thus, the overall social surplus declines because the decrease in consumer surplus surplus is greater than the increase in producer surplus.

For example,

Consumer Surplus at equilibrium: G+H+J

Producer Surplus at equilibrium: I+K

Consumer Surplus at Price Floor: G

Producer Surplus at Price Floor: H+I

As from the figure, when a price floor is imposed, the producer surplus increases from I+K to I+H (areaH > areaK)

But, the consumer surplus reduces from G+H+J to G (i.e. consumer loses H+J)

Net Social Surplus changes from G+H+J+I+K to G+H+I

Lost Social Surplus is J+K (the Deadweight loss to the society)

Hence,

Producer surplus though increases, but the lost consumer surplus is greater. Hence, the net effect in terms of the overall social surplus reduces.