The following problem was assigned by Kevin Murphy in Economics 301 at the University of Chicago during the Autumn quarter of 2008. Marshall Steinbaum, Friend of Economics in the Rear-view Mirror and Research Director at the Roosevelt Institute), provided a copy to share here with the history of economics community.
Marshall Steinbaum writes:
Gary Becker and Kevin Murphy would each give one lecture per week. Every weekly problem set had two questions, one assigned by Becker and one by Murphy. This one on unions was Murphy’s, as indeed were all the ones with a vaguely macro cast to them. It was odd how he both denigrated macro in lectures and assigned a whole shadow macro curriculum.
The problem below can be profitably read in light of the contemporary discussion of monopsony power and unions (e.g. Kate Bahn, “Understanding the importance of monopsony power in the U.S. labor market,” Equitable Growth, July 5, 2018)
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Links to 1947 Harvard syllabi on unions
Looking back in the rear-view mirror a half-century earlier, it is interesting to note the depth of coverage of unions in the graduate labor sequence at Harvard taught by John Dunlop:
Economics 81a Labor Organization and Collective Bargaining
Economics 81b Labor and Public Policy
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Problem by Kevin Murphy on unions (2008)
Consider the impact of unions on wages. Consider a simple economy with a fixed supply of labor, L, which is supplied inelastically. Assume that there is a union that sets wages for workers covered by the union contract so as to maximize the income of its members. Assume that there are three inputs to production, L1, L2 and K. All workers are identical and can provide either type 1 or type 2 labor. Capital is supplied in a competitive market. Assume that all prices are denominated in terms of the output good Y.
- If the production function has the form Y=F(K,G(L1,L2)), where both F() and G() are CRS, how would a union that can set wages for L1and L2 desire to set wages? Might the union want to set wages at the competitive level? Would the union want to set equal wages for the two types of labor? Why or why not?
- How would your answer to A change if the production function was Y=H(K,L1,L2), where H was CRS?
- What would happen in parts A and B if the supply of capital was perfectly elastic? Why?
- Now assume that markets are initially competitive which results in competitive prices and usage for each type of labor and capital. Assume that those working as type 2 workers form a union so that they can increase their incomes. In particular assume that the newly formed union seeks to maximize the incomes of its initial members. Under the assumption of part A, how would the union set the wage for type 2 labor? What effect would this have on overall labor income? Could it make workers as a whole worse off? If so when and why?
- Now assume that there is only one type of labor so that Y=F(L,K) with F() having CRS. Assume that the union is free to set the real wage picks a wage that will maximize the current income of workers and that the demand for labor is inelastic at the steady state wage rate. Assume that the capital stock is fixed initially but that capital is accumulated via investment as in the neo-classical growth model. If we start at the steady state of the neoclassical growth model, what will happen to wages, capital and employment over time? Why?
Source: Transcribed from a personal copy of Marshall Steinbaum made available to Economics in the Rear-view Mirror.
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Marshall Steinbaum added
“In this case, I believe the point is that when the union causes labor to be paid in excess of its marginal product, the rate of return on capital is driven lower than the capitalists’ rate of time preference, causing them to cease to supply capital. As the capital stock depreciates away, the labor share remains high even as the wage level declines, causing a downward spiral rather than re-equilibration at a lower level of capital and output.
These problem sets were never explicitly tied to real-world events, but the sense I got was that this was intended to be a theory of the declining manufacturing sector in the United States and Western Europe.”
Source: Personal communication.
Image Source: Kevin Murphy in “Chicago Schooled” by Michael Fitzgerald, University of Chicago Magazine (September-October, 2009).