A3-10. Part 2. Suppose the short run total cost functions for all existing and p

Question

A3-10. Part 2. Suppose the short run total cost functions for all existing and potential firms in a competitive industry are given by: TC = 100 + 10q + q2, where q is the output level of the firm in a given period. This means that MC = 10 + 2q.

(c) What does the MC curve tell us about the marginal product (MP) of the firm’s variable factor of production (presumably labour)? [4]

(d) What is the firm’s profit maximizing output at the following prices: 5, 20, 30, and 40? What is the level of profits at each of the prices? [8]

(e) Now assume that all existing and potential firms have the same cost function and that the minimum point on the short-run ATC is also the minimum point on long-run average cost (LRAC). Briefly explain why only one of the prices identified in part (d) is a long-run equilibrium price. [4]

Explanation / Answer

c).

Consider the given problem, as we know that the “MC” is the addition cost if we increase “Q” by 1 unit, so we can also express it in terms of “MP”, let’s say “L” be the variable factor then “MC=W/MPL”, so there is negative relationship, => as “MPL” increases => “MC” decreases, on the other hand as “W”, the cost of “L” increases => “MC” increases.

d).

Here the TC function is given by, “TC=100+10*q+q^2”. So, AVC=10+q and MC=10+2*q.

So, the minimum of AVC is “10” at “q=0”. So now if “P=5 < 10”, optimum “q” is “0”, so the profit is “P*q – c”, => “-100”.

Now, if P=20 > 10, then the optimum “q”, will be determined by “MC=P”, => “10+2*q=20”, => 2*q = 10, => q=10/2=5. So, the optimum “q=5”.

So, at q=5, the optimum profit be “p*q – c = 20*5 – (100+10*5+5^2)”.

=> 100 – 175 = (-75) < 0.

Now, if P=30 > 10, then the optimum “q”, will be determined by “MC=P”, => “10+2*q=30”, => 2*q = 20, => q=20/2=10. So, the optimum “q=10”.

So, at q=10, the optimum profit be “p*q – c = 30*10 – (100+10*10+10^2)”.

=> 300 – 300 = 0.

Now, if P=40 > 10, then the optimum “q”, will be determined by “MC=P”, => “10+2*q=40”, => 2*q = 30, => q=30/2=15. So, the optimum “q=15”.

So, at q=15, the optimum profit be “p*q – c = 40*15 – (100+10*15+15^2)”.

=> 600 – 475 = 125 > 0.

e).

We can see that there “4”, possible prices and only at “P=30”, the economic profit is “0”, and we also know that at the LR equilibrium under perfect competition the economic profit is “0”,. So “P=30” be the LR equilibrium price here.

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