Microeconomics Question on Production Functions

BrumCo is a firm that produces heaters in a perfectly competitive market. The production of each model train requires plaster (P), and grams of white paint (W). Their production function is given by

f(P,W)= min{6sqrt(P), 3W-12}

(a)  Draw the isoquant corresponding to q = 48 heaters in a clearly labelled diagram where P is the horizontal axis and W is the vertical axis. Label two distinct input bundles (P, W ) in the diagram which give q = 48.


(b) Compute the marginal products of each input.


(c) Does this production function exhibit constant returns to scale? Using the marginal products you have computed in the previous part, explain your answer in no more than 25 words.


(d)  Suppose that BrumCo wants to produce q heaters when the price of plaster is $72/mL
and the price of white paint is $18/g. Show that the minimum cost of such an undertaking is

c(q)=2q^2 +6q+72.

(e)  Suppose that the market price is p, and BrumCo will produce q units of heaters. Using the cost function you found in the previous part, find the supply function of BrumCo. Express it as a function of price.

(f)  Suppose that there are 60 identical firms like BrumCo who act as price-takers and the market demand for model trains is given by

QD =910−5p.

Show that the short-run market equilibrium price in this industry is p∗ = 50.

(g) In the long run, given no shocks to market demand, do you expect to see the number of firms in this industry increase, decrease or stay the same?


(h)  Assuming no shocks to market demand, what is the largest whole number of firms that this market can sustain in the long run equilibrium?


(i)  Suppose that we are in the long-run equilibrium given in the previous part. Now, 20 of the firms successfully lobby the government for a subsidy of $5 per heater sold. How many firms will there now be in the long run equilibrium?


Thank you and please show working when you can.

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Mathe Mathe
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  • Hi sorry just wanted to clarify that for the last part, its just 20 firms that receive the subsidy. Is the answer still correct? For part i

    • Mathe Mathe
      0

      Hi, no, that's not the correct answer. 1. From the problem, we infer that all firms recieve the subsidy. 2. The new equilibrium price (to the public) is 20. 3. 130 firms participate in this industry,

  • Hi thanks for the response, sorry I can't reply to your reply. I'm just a bit confused because I was told that only 20 of the firms receive the subsidy. Does this not affect the answer and it remains unchanged? Thanks again :)

    • Mathe Mathe
      0

      From my understanding of the problem, 20 firms made part of a lobby to get a subsidy for the whole industry. It's not clear from the problem that only 20 firms would get the subsidy.

  • Yea I thought so too but my professor clarified that only 20 firms received the subsidy. Do you think you could send the working out for if only 20 firms received the subsidy?

    • Mathe Mathe
      +1

      I think I could, but let me tinker about it. For a moment.

    • Mathe Mathe
      0

      I just added a new document (with the same name) answering to this question.

  • Amazing thank you!

The answer is accepted.
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