Q 2. Hilal Industries manufactures floppy disks that consumers perceive as ident

Question

Q 2. Hilal Industries manufactures floppy disks that consumers perceive as identical to those produced by numerous other manufacturers. Recently, Hilal hired an econometrician to estimate its cost function for producing boxes of one dozen floppy disks. The estimated cost function is C 20+ 2Q2. Show all your calculations a. What are the firm's fixed costs (TFC) and marginal cost (MC)? Now suppose other firms in the market sell the product at a price of $10. b. How much should this firm charge for the product? Why? c. What is the optimal level of output to maximize profits? d. How much profit will be earned? e. In the long run, should this firm continue to operate or shut down? Why? Draw the demand, MR, MC curves and show profit maximizing output, price, total profit in the graph using the data above f.

Explanation / Answer

Cost Function for firm is C = 20+2Q^2

If we break the cost function we know cost which in invariant or doesnt change with quantity produced is fixed cost and variable cost is propotional to quantity produced.

Hence TFC is 20 & Marginal Cost is dC/dQ = 4Q = MC

Revenue is P* Q if Price of P is chosen hence MR=P

MR = MC

P = 4Q

Now Profit Function will be revenue -cost = P*Q - C =4Q^2 - 20-2Q^2 = 2Q^2-20

Differentiating Profit Function with Q is 4Q-20 and optimum level of Q is 5 as 4Q - 20 = 0

Hence P= 4Q=20 for maximum profit

Profit Function is 2Q^2-20 to breakeven when equal to 0

therfore Q^2 = 10 and Q = 3.24 hence Q>3 to earn positive profit

hence Price should be set at P > 4*sqrt(10)

Optimum level of output as calculated above is Q = 5

Price is set to 20 for given cost function

With Q = 5 Profit would be 4Q^2 -20-2Q^2 = 2Q^2-20 = 30

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