Suppose Acme Nuts & Bolts provides prepackaged assortments of nuts and bolts in
ID: 1213692 • Letter: S
Question
Suppose Acme Nuts & Bolts provides prepackaged assortments of nuts and bolts in various sizes and operates in a perfectly competitive market where there are a total of 10 firms. Basically, all the firms in this competitive market have technologies (production and cost conditions) that are the same as Acme’s). Suppose Acme’s total cost function is given by:
C(q)=500+5q+0.2q^2
a. Calculate Acme’s optimal output level and profits if the marketinverse demand for cases of the product is stable and given by: P=50-0.032Q
b. If Acme is typical of the firms in this industry, calculate the long-run equilibrium output, price and profit level that will ultimately prevail in this industry.
Explanation / Answer
Answer:
Acme’s total cost function is: C(q)= 500+5q+0.2q2
a. Calculate Acme’s optimal output level and profits if the market inverse demand for cases of the product is stable and given by: P = 50-0.032Q
We know in perfect competitive market P = MC. So we can find MC first
MC = dTC/dQ = 0.4q + 5
Therefore, P = MC = 0.4q + 5
Now, 0.4 Q + 5 = 50-0.032Q
0.432 Q = 55
Q = 104.16
We can substitute Q = 104.16 into the TC and MC functions then we get:
TC = 500 + 5q + 0.2q2
TC = 500 + 5 (104.16) + 0.2(104.16)2
TC = $3190.66
P = MC = 0.4(104.16) + 5
Therefore, P = $46.66
Profit = TR – TC
TR = P*Q = $46.66*104.16 = $4860.10
Profit = $4860.10 - $3190.66
Profit = $1669.44
Therefore, Acme is making an economic profits in the short-run at the optimum output and price is Q = 104.16 and P = $46.66.
b. If Acme is typical of the firms in this industry, calculate the long-run equilibrium output, price and profit level that will ultimately prevail in this industry.
Acme’s firm is perfect competitive, so the economic profit ultimately becomes zero in the long run. That is at equilibrium point the price and the quantity will be optimum and the economic profits equal to zero in the long-run situation in perfect competitive market.
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