To find the producer surplus and consumer surplus, we need to understand their definitions and then calculate them based on the given demand and supply functions.

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**Producer Surplus (PS):**

Producer surplus represents the difference between the actual price a producer receives in the market and the minimum price they would be willing to accept for the quantity supplied. The formula for producer surplus is given by the integral of the supply function (s(q)) from 0 to the equilibrium quantity (Q*) where demand equals supply. [ PS = \int_0^{Q^*} s(q) \, dq ] In this case, ( s(q) = 5.2q ), and we need to find the equilibrium quantity (Q*) by setting demand equal to supply: ( -0.8q + 150 = 5.2q ).**Consumer Surplus (CS):**

Consumer surplus represents the difference between the maximum price a consumer is willing to pay and the actual price they pay in the market. The formula for consumer surplus is given by the integral of the demand function (d(q)) from 0 to the equilibrium quantity (Q*). [ CS = \int_0^{Q^*} d(q) \, dq ] In this case, ( d(q) = -0.8q + 150 ), and again, we use the equilibrium quantity found earlier.

After finding the equilibrium quantity, you can calculate both the producer surplus and consumer surplus using the appropriate integrals.