Consider a Firm That Uses Labor and Capital to Produce

question 23

Essay

Consider a firm that uses labor and capital to produce output x using a homothetic production technology that has increasing returns to scale when output lies between 0 and x_A, constant returns to scale when output lies between x_A, and x_B, and decreasing returns to scale when output exceeds x_B (where 0<x_A<x_B).Although the different parts of the question repeatedly refer to the isoquant graph you first draw in (a), you should probably re-draw the graph several times - each time only with the portions you need for the question -- to indicate the different items that are asked for in the remaining parts of the question (rather than indicating all your answers on literally the same graph).
a.On a graph with labor on the horizontal and capital on the vertical axis, draw isoquants for x_A and x_B.For a given set of input prices w and r, indicate the least cost input bundle A=(l^A, k^A) for producing x_A using an isocost line.Label the slope of the isocost line and then label the slope of the isoquant in terms of the marginal product of labor and capital.
b.Indicate where the least cost input bundle B for producing x_B must lie (in light of the homotheticity property of the production technology.) What does the vertical slice along which all cost-minimizing input bundles lie look like (on a graph with "inputs" on the horizontal and x on the vertical)?
c.Indicate all input bundles in your isoquant graph that could be part of a profit maximizing production plan for some output price p>0.
d.Suppose the actual profit maximizing production plan is (l*,k*,x*).What two conditions involving the marginal products of the inputs hold at this - and only this - production plan?
e.Now suppose that a change in tax policy results in an increase of the rental price of capital r.Indicate all possible input bundles in an isoquant graph that might be long-run profit maximizing assuming no change in p or w.(Include the isoquant corresponding the initial profit maximizing output level x* as well as the isoquant that contains B (from (b)) in your graph.) Explain your reasoning.f.Pick one input bundle that lies in the region you indicated in part (e) as the new profit maximizing input bundle (assuming only r changes) and assume that it is the long-run profit maximizing input bundle after the increase in r (not considering any possible change in p that might result as firms enter and exit the industry).Call the production plan associated with that input bundle C=(lC, kC, xC).Suppose this firm is one of many identical firms in a competitive market, and suppose that, prior to the increase in r, the market was in long run equilibrium.Suppose further that we observe the number of firms in the market increases as a result of the increase in r.Indicate in an isoquant graph all input bundles that might be profit maximizing after the market has reached its new long run equilibrium? (Include in this graph the isoquants for xC as well as for x*.)

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Definitions:

Dishonored Note

A promissory note that has not been paid by the maker at maturity, resulting in a default.

Collection Efforts

Activities undertaken by a business or organization to pursue and receive payments owed by customers or clients.

Reversing Entries

Journal entries usually made at the beginning of an accounting period to reverse or cancel out adjusting entries from the end of the previous period.

Allowance Method

An accounting technique used to anticipate and adjust for potential future losses from uncollectible accounts receivable.