Workers as Producers of Consumption: We can see some of the connections between consumer and producer theory by re-framing models from consumer theory in producer language.
A: Suppose we modeled a worker as a “producer of consumption” who can sell leisure of up to 60 hours per week at a wage w.
(a) On a graph with “labor” as the input on the horizontal axis and “consumption” as the output on the vertical, illustrate what the producer choice set faced by such a “producer” would look like.
(b) How is this fundamentally different from the usual producer case where the producer choice set has nothing to do with prices in the economy?
(c) What does the marginal product of labor curve look like for this “producer”?
(d) On the graph you drew for part (a), illustrate what “producer tastes” for this producer would look like assuming the worker’s tastes over consumption and leisure satisfy the usual five assumptions for tastes we developed in Chapter 4. How is this fundamentally different from the usual producer case where the producer’s indifference curves are formed by prices in the economy?
B: Suppose the worker’s tastes over consumption and leisure are Cobb-Douglas with equal weights on the two variables in the utility function.
(a) Derive an expression for the production function in this model.
(b) Set up the worker’s optimization problem similar to a profit maximization problem for producers.
(c) Derive the “output supply” function—i.e. the function that tells us how much consumption the worker will “produce” for different economic conditions.