Social entrepreneurs are entrepreneurs who use their talents to advance social causes that are typically linked to the provision of some type of public good. Their challenge within the civil society is, in part, to motivate individuals to give sufficient funding to the projects that are being advanced. Aside from lobbying for government aid, we can think of two general ways in which social entrepreneurs might succeed in increasing the funding for their organizations. Both involve marketing — one aimed at increasing the number of individuals who are aware of the public good and thus to increase the donor pool, the other aimed at persuading people that they get something real out of giving to the cause.
A: We can then think of the social entrepreneur as using his labor as an input into two different single-input production processes—one aimed at increasing the pool of donors, the other aimed at persuading current donors of the benefits they get from becoming more engaged.
(a) Suppose that both production processes have decreasing returns to scale. What does this imply for the marginal revenue product of each production process?
(b) If the social entrepreneur allocates his time optimally, how will his marginal revenue product of labor in the two production processes be related to one another?
(c) Another way to view the social entrepreneur’s problem is that he has a fixed labor time allotment L that forms a time budget constraint. Graph such a budget constraint, with ℓ1 — the time allocated to increasing the donor pool — on the horizontal axis and ℓ2 — the time allocated to persuading existing donors—on the vertical.
(d) What do the isoquants for the two-input production process look like? Can you interpret these as the social entrepreneur’s indifference curves?
(e) Illustrate how the social entrepreneur will optimize in this graph. Can you interpret your result as identical to the one you derived in (b)?
(f) Within the context of our discussion of “warm glow” effects from giving, can you interpret ℓ2 as effort that goes into persuading individuals that public goods have private benefits?
(g) How might you re-interpret this model as one applying to a politician (or a “political entrepreneur”) who chooses between allocating campaign resources to mass mailings versus political rallies?
(h) We discussed in the text that sometimes there is a role for “tipping points” in efforts to get individuals engaged in public causes. If the social entrepreneur attempts to pass such a “tipping point”, how might his strategy change as the fundraising effort progresses?
B: Suppose that the two production processes introduced in part A are f1 (ℓ1) and f2 (ℓ2), with d fi /dℓi < 0 for i = 1, 2 and with “output” in each process defined as “dollars raised”.
(a) Assuming the entrepreneur has L hours to allocate, set up his optimization problem. Can you demonstrate your conclusion from a (b)?
(b) Suppose f1 (ℓ1) = Alnℓ1 and f2 (ℓ2) = B lnℓ2 with both A and B greater than 0. Derive the optimal ℓ1 and ℓ2.
(c) In equation (27.54), we determined the individual equilibrium contribution in the presence of a warm glow effect. Suppose that this represents the equilibrium contribution level for the donors that the social entrepreneur works with—and suppose I = 1,000, α = 0.4, β = 0.6. In the absence of any efforts on the part of the entrepreneur, N = 1000 and γ = 0.01. How much will the entrepreneur raise without putting in any effort?
(d) Next, suppose that N (ℓ1) = 1000(1+ℓ11/2) and γ (ℓ2) = 0.01(1+ℓ1/2 2), and suppose that the entrepreneur has a total of 1,000 hours to devote to the fundraising effort. Assume that he will in fact devote all 1,000 hours to the effort, with ℓ2 therefore equal to (1000−ℓ1). Create a table with ℓ1 in the first column ranging from0 to 1000 in 100 hour increments. Calculate the implied level of ℓ2, N and γ in the next t three columns, and then report the equilibrium level of individual contributions zeq and the equilibrium overall funds raised yeq in the last two columns. (Obviously this is easiest to do by programming the problem in a spreadsheet.)
(e) Approximately how would you recommend that the entrepreneur split his time between recruiting more donors and working with existing donors?
(f) Suppose all the parameters of the problem remain the same except for the following: γ = 0.01(1+ℓ0.5 2 +0.001N1.1). By modifying the spreadsheet that you used to create the table in part (d), can you determine the optimal number of hours the entrepreneur should put into his two fundraising activities now? How much will he raise?