Question

2. Suppose that a firm faces the demand curve, P 300-4Q, where P denotes price in dollars and Q denotes total unit sales. The cost equation is TC 300 +92Q. a.Determine the firm's profit-maximizing output and price. 2 points b. Gven the output (Q) value from part a, compute Total cost and Marginal cost when the cost equation is TC 300 +92Q: 1 point c. Suppose that there is a change in the production process so that the cost equation becomes TC 1,800+100+Q2. Compute the new Total cost and Marginal cost at the same output level (Q value) from part a: 1 point d. Determine the firm's new output and price level when the cost equation is TC 1,800+ 100 Q2 and the demand curve remains P 300-40 2 points e. Using your answers to part b and c, explain why the profit maximizing quantity changed in your answers to part a and part d: 1 point

Answer 1

[As HOMEWORKLIB’s policy and guideline, the first-four related parts are answered below:]

2.

a.

Here the demand curve is downward slopping, since there is a variable part in the demand equation. Therefore, the profit-maximizing condition is (MR = MC).

MR comes from the demand function.

P = 300 – 4Q

TR = P × Q = 300Q – 4Q^2

MR = Derivative of TR with respect to Q

       = 300 – 8Q

MR comes from the TC function.

TC = 300 + 92Q

MC = Derivative of TC with respect to Q

       = 0 + 92

       = 92

Now by applying the condition,

MR = MC

300 – 8Q = 92

8Q = 208

Q = 208/8 = 26

Now by putting this value in the demand function, we will get the price.

P = 300 – 4Q

   = 300 – 4 × 26

   = 300 – 104

   = 196

Answer: Output is 26 units and price is 196.

b.

TC = 300 + 92Q

TC = 300 + 92 × 26

      = 300 + 2392

      = 2692 (Answer)

MC = 92 (Answer)

c.

TC = 1,800 + 10Q + Q^2

      = 1800 + 10 × 26 + 26^2

      = 1800 + 260 + 676

      = 2736 (Answer)

TC = 1,800 + 10Q + Q^2

MC = Derivative of TC with respect to Q

       = 0 + 10 + 2Q

       = 10 + 2 × 26

       = 10 + 52

       = 62 (Answer)

d.

MR = MC

300 – 8Q = 62

8Q = 238

Q = 238/8 = 29.75

Now by putting this value in the demand function, we will get the price.

P = 300 – 4Q

   = 300 – 4 × 29.75

   = 300 – 119

   = 181

Answer: Output is 29.75 units and price is 181.