Question

Urgently required ( only d,e ,f ,g,h,i)

A monopoly firm faces a demand curve given by the following equation: P = $500 − 10Q, where Q equals quantity sold per day. Its marginal cost curve is MC = $100 per day. Assume that the firm faces no fixed cost. You may wish to arrive at the answers mathematically, or by using a graph (the graph is not required to be presented), either way, please provide a brief description of how you arrived at your results.

a)   How much will the firm produce?b)   How much will it charge?c)   Can you determine its profit per day? (Hint: you can; state how much it is.)d)   Suppose a tax of $1,000 per day is imposed on the firm. How will this affect its price?e)   How would the $1,000 per day tax its output per day?f)   How would the $1,000 per day tax affect its profit per day?g)   Now suppose a tax of $100 per unit is imposed. How will this affect the firm’s price?h)   How would a $100 per unit tax affect the firm’s profit maximizing output per day?i)   How would the $100 per unit tax affect the firms profit per day?

Answer 1

(d) and (e)

A daily tax is a fixed cost. Increase in fixed cost doesn't change MC, so the firm's Price and Output remains unchanged.

(f)

Using given information, when profit is maximized,

P = $300

Q = 20

TR = PQ = 300 x 20 = $6,000

TC = FC + Q x MC = 1,000 + 20 x 100 = 1,000 + 2,000 = $3,000

Profit = TR - TC = $6,000 - $3,000 = $3,000

Therefore, profit will decrease by $1,000 per day.

(g) and (h)

The output tax will increase MC by $100 and new MC = 100 + 100 = $200

Setting MR = new MC,

500 - 20Q = 200

20Q = 300

Q = 15 [Output will decrease by (20 - 15) = 5]

P = 500 - 10 x 15 = 500 - 150 = $350 [Price paid by buyers will increase by (350 - 300) = $50]

(i)

TR = 350 x 15 = $5,250

TC = Q x MC = 15 x 200 = $3,000

Profit = 5,250 - 3,000 = $2,250 [Profit will decrease by (4,000 initial profit - 2,250) = $1,750]