# Return to the setting of Example 4.2, but now assume the firm must pay, at time t = 0, a…

Return to the setting of Example 4.2, but now assume the firm must pay, at time t = 0, a franchise fee of 850 in order to legally produce and sell its products. Further assume it adopts precisely the same production plan. Determine its economic income and accounting income for each of the two periods. Also verify that this production plan is indeed optimal.

((Example 4.2 Return to the setting of Examples 3.5 and 3.6. The product spot prices are P1 = 44 and P2 = 60.5, and the spot factor prices are P1 = 20, P3 = 5 and P2 = 16.5. The interest rate is r = 10%, and the common factor is limited to a maximum of z3 = 15. Further assume the firm follows the previously identified profit maximizing path by producing and selling q 1 = 15 in the first period and q 2 = 25 in the second period, while consuming factor quantities of z 1 = 15, z 2 = 41.667 and z 3 = 15. In present value terms, revenue is

So the firms profit is R −C(q ; P) = 1, 850−1, 000 = 850, a familiar number for sure. And this leads to the cash flow summarization originally displayed in Table 3.3, and reproduced below. The cash flows total

Also notice the constant rate of return calculation and the fact

CF0+CF1+ CF2 = 1, 110 = I0 + I1 + I2. This is all summarized as follows.

Though this is wearing thin you should ponder the fact that even though the firm’s activities are not separable, and that includes the firm’s cost curve, the economist has no difficulty divining the period-by-period economic income. This is not witchcraft; no, it reflects the fact economic income is the factor cost of funds provided the enterprise. The market price of these funds is known, this is the interest rate r; and the amount of these funds is equally well known, this is the continuation present value, P Vt.

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