Second look enterprises (SLE) buys old computers, fixes them up, and resells them. Its weekly revenue function is R = 70q − 2q2 ,so its marginal revenue is MR = 70 − 4q. Its weekly cost function is C = 10q + 22, so its marginal cost is MC = 10 + 2q.
a. Use excel to calculate SLE's revenue, cost, and profit for q= 1 to q = 30 in increments of 1. SLE's manager wants to maximize profit. Based on these calculations, what output does the manager choose? Create columns in your spreadsheet for MR and MC and verify that MR = MC at the profit-maximizing output level.
b. Now assume that SLE is run by a manager who is paid 10% of the revenue and therefore wants to maximize revenue. How much output does the firm produce now? What is marginal revenue at this output? Explain.
c. Now suppose that SLE is acquired and managed by a philanthropist who wants to promote recycling of used computers and therefore produces as much output as possible as long as the firm does not make losses. What output does SLE produce now? Explain.
d. The shareholders of the firm hire a manager on a profit-sharing basis whose payment, M, is 25% of the firm's profit: M = 0.25(R − C).The shareholders receive the remaining 75%,so their income is S= 0.75(R − C). Add columns for M and S to the spreadsheet and calculate the manager's payment and the shareholders' income for q = 1, 2, ... , 30. Determine the amount of output that manager will produce if the manager's objective is to maximize his or her own compensation. Is this outcome consistent with the shareholders' profit maximizing objective? Explain.
A) MR = 70-4Q
MC = 10+2Q
MR = MC for profit maximisinf output
10+2q = 70-4q
Q = 10
R = 70q -2q2
Dr/dq = 0
Q = 17.5
MR =0 at this output as any more output produces after thia would yield a negative MR
C) As it is run by a philanthropist,
R - C =0
70q -2q2 -10q - 22 =0
60q - 2q2 -22=0
2q2 - 60q + 22 =0
Q = 29.6 = 30
D) Manager's pay = 0.25(R-C)
Shareholder's pay = 0.75(R-C)
R-C = -2q2+60q-22 =
d/dq = 0 for maximization
Q = 15
When q = 15 the manager's compensation is maximised and so is the shareholder's objective as both of their revenue depends on profit.
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