This is an advanced microeconomics question; Below is a production function for

Question

This is an advanced microeconomics question;

Below is a production function for a firm that turns two variable factors of production, capital k and labor l, into a single output y. Labor is freely variable in the short and long run. Capital is fixed in the short run, but can be varied in the long run. Assume that the firm is a price taker in the factor markets, that the price of capital is r, and the price of labor is w. For each of the production function, what is the firm's long-run total (variable) cost function? In the short and in the long run, does the firm exhibit increasing, decreasing, or constant returns to scale?

(a) f(k,l) = ak + (1 - a)l

Explanation / Answer

Production Function for firm - 2 variable factors of production- capital -k n l i.e. k+l=y (o/p)

Short Run- Fixed:K, Variable:L, Production wld increase when more units of variable factors are used with the fixed factor. Law of variable proportion comes under short run PF.

Long Run: All Variable factors- L,K.In long run production can be increased by increasing units of all factors simultaneously & in the same proportion. Law of returns to scale comes under long run PF

While assuming firm is a price taker means it applies to perfectly competitive market;where kp -(price of k)-r & Lp -(price of l) - w.

In the short run PF- returns to one input-o/p relationship is also kwn as the law of non-proportional returns / the law of the diminishing Marginal retun.in this case keeping scare factor constant i.e.K, n L- variesimplies that the increased addup units of a variable inputs while quantities of the other inputs that are held constant , the increase in TP(Total Production) becomes after some point smaller n smaller.Therefore , law of diminishing returns operates in short run PF while

In the long run it is subject to whether the proportionate change in o/p equals ,exceeds,or falls short of the proportionate change in both inputs, PF is classified as constant, decreasing( & increasing returnn to scale.

As the plant size increases economies of scales operates where Long run average cost curve ;also kwn as planning curve pervades. Firms LAC ia so drawn as to be tangent to each of the short run average cost curve since an infinite number of short- run average cost curve ia assumed, every point on the long run ACC will be at the point of tangency point with some short run average cost curve. if a firm desires to produce a particular 0/p in the long run it will pick a point on the long run average cost curve to that o/p & it will build a relevant plant & operates on the corresponding short run average cost. The long run ACC reveals to the firm how large should be the plant for producing a certain o/p at the least posible cost.

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