is this Step 1: Deriving the Total Cost Function C ( y ) C(y) From the second condition S M C ( 0 ) = A V C ( 0 ) = 1 SMC(0)=AVC(0)=1, we know that at zero output, both the marginal cost and the average variable cost are equal to 1. This suggests that the fixed costs are likely zero because the average variable cost at zero output reflects only variable costs. Now, let's start by using the relationship between the cost functions: Total Cost (TC) is composed of Fixed Costs (FC) and Variable Costs (VC): C ( y ) = F C + V C ( y ) C(y)=FC+VC(y) Since SMC is the derivative of TC with respect to y y, we know that: S M C ( y ) = d C ( y ) d y SMC(y)= dy dC(y) Given that S M C ( 0 ) = 1 SMC(0)=1, this tells us that the slope of the total cost curve is 1 when output is 0. This suggests a linear relationship for the marginal cost function. Form of the Marginal Cost Function: We can express the marginal cost as a linear function: S M C ( y ) = c + d y SMC(y)=c+dy Where c c and d d are constants. From S M C ( 0 ) = 1 SMC(0)=1, we know that: S M C ( 0 ) = c = 1 SMC(0)=c=1 So, the marginal cost function becomes: S M C ( y ) = 1 + d y SMC(y)=1+dy To find the exact form of SMC, we need more information or a relationship between S M C SMC and AC. For now, let's assume the simplest linear form S M C ( y ) = 1 + y SMC(y)=1+y (where d = 1 d=1) for simplicity, as it satisfies the condition S M C ( 0 ) = 1 SMC(0)=1. is this a right way to solve